Summary
# Measurements and motion
This topic introduces fundamental concepts in physics related to measurement, including units, powers of ten, length, area, volume, mass, time, systematic errors, and precision measuring instruments [15](#page=15).
### 1.1 Units and basic quantities
Before any measurement can be made, a standard unit must be chosen. The size of the quantity is then determined using an instrument with a scale marked in that unit. The three fundamental quantities measured in physics are length, mass, and time, with units for other quantities being derived from these. The International System of Units (SI) is a metric system used globally, characterized by decimal divisions and multiplications by 10 for different units [15](#page=15).
### 1.2 Powers of ten shorthand
Powers of ten provide a concise way to express very large or very small numbers. This notation, also known as standard notation, uses a number multiplied by a power of 10 [15](#page=15).
* $4000 = 4 \times 10^3$ [15](#page=15).
* $400 = 4 \times 10^2$ [15](#page=15).
* $40 = 4 \times 10^1$ [15](#page=15).
* $4 = 4 \times 10^0$ [15](#page=15).
* $0.4 = 4 \times 10^{-1}$ [15](#page=15).
* $0.04 = 4 \times 10^{-2}$ [15](#page=15).
* $0.004 = 4 \times 10^{-3}$ [15](#page=15).
The exponent indicates how many times the number is multiplied by 10 (if positive) or divided by 10 (if negative) [15](#page=15).
### 1.3 Length
The SI unit of length is the metre (m). Submultiples include the decimetre (dm, $10^{-1}$ m), centimetre (cm, $10^{-2}$ m), millimetre (mm, $10^{-3}$ m), micrometre (µm, $10^{-6}$ m), and nanometre (nm, $10^{-9}$ m). A multiple for larger distances is the kilometre (km, $10^3$ m) [15](#page=15).
> **Tip:** When using a ruler, ensure your eye is directly over the mark to avoid parallax error [15](#page=15).
To obtain an average value for small distances, multiple instances can be measured and then divided. For example, measuring the distance of five waves in a ripple tank and dividing by five gives the average wavelength [16](#page=16).
### 1.4 Significant figures
Significant figures indicate the precision of a measurement. More significant figures should not be given than are justified by the limitations of the apparatus and the experimenter [16](#page=16).
* A measurement of 4.5 has two significant figures [16](#page=16).
* 0.0385 has three significant figures, with 3 being the most significant and 5 the least certain [16](#page=16).
When performing calculations, the answer should have the same number of significant figures as the least precise measurement used. To round a number, if the next digit to the right is less than 5, the last significant figure remains unchanged; if it is 5 or greater, the last significant figure is increased by one. In standard notation, the number of digits before the power of ten determines the significant figures (e.g., $2.73 \times 10^3$ has three significant figures) [16](#page=16).
### 1.5 Area
The area of a square with sides of length $l$ is $l^2$, and for a rectangle with length $l$ and breadth $b$, the area is $l \times b$. The SI unit of area is the square metre ($m^2$) [16](#page=16).
* $1 m^2 = 10000 cm^2 = 10^6 mm^2$ [16](#page=16).
The area of a triangle is given by $\frac{1}{2} \times \text{base} \times \text{height}$. The area of a circle with radius $r$ is $\pi r^2$, and its circumference is $2\pi r$, where $\pi \approx 22/7$ or $3.14$ [16](#page=16) [17](#page=17).
### 1.6 Volume
Volume is the amount of space occupied by an object. The SI unit is the cubic metre ($m^3$), but the cubic centimetre ($cm^3$) is often used [17](#page=17).
* $1 m^3 = 10^6 cm^3$ [17](#page=17).
For a rectangular block, volume is calculated as length × breadth × height. The volume of a sphere of radius $r$ is $\frac{4}{3}\pi r^3$, and the volume of a cylinder of radius $r$ and height $h$ is $\pi r^2 h$ [17](#page=17).
Liquid volumes can be measured using measuring cylinders or burettes. When reading these instruments, the eye must be level with the bottom of the meniscus (the curved surface of the liquid), except for mercury where the top is read. Liquid volumes are also expressed in litres (l), where $1$ litre $= 1000 cm^3 = 1 dm^3$, and $1$ millilitre (ml) $= 1 cm^3$ [17](#page=17).
### 1.7 Mass
Mass is the measure of the amount of matter in an object. The SI unit of mass is the kilogram (kg). The gram (g) is one-thousandth of a kilogram ($1 kg = 1000 g$) [17](#page=17).
> **Important Distinction:** Mass and weight are distinct concepts in science, although the term "weight" is often used colloquially when mass is meant. Mass is measured on balances, such as beam balances or digital top-pan balances [17](#page=17).
### 1.8 Time
The SI unit of time is the second (s). Modern clocks and watches use oscillations from quartz crystals or caesium atoms for accuracy [18](#page=18).
> **Tip:** To improve accuracy when measuring time intervals, time several oscillations rather than just one [18](#page=18).
For experiments, it's important to choose a timer accurate enough for the task; a stopwatch is suitable for a pendulum's period, but a clock measuring milliseconds is needed for faster events. Digital clocks triggered by electronic signals are useful for very short time intervals [18](#page=18).
### 1.9 Systematic errors
A systematic error is an error introduced by the measuring system itself, leading to consistent deviations from the true value. For example, a ruler with a gap before the zero mark will consistently underestimate heights by the length of that gap. Using a ruler with the zero at the end can avoid this specific error. Holding a measuring rule at an angle to the vertical also introduces a systematic error [18](#page=18) [19](#page=19).
### 1.10 Vernier scales and micrometers
For measurements requiring greater accuracy than a standard ruler (approximately 1 mm), vernier calipers and micrometer screw gauges are used [19](#page=19).
#### 1.10.1 Vernier scales
A vernier scale is a small sliding scale that allows for more precise readings. A common type measures to 0.01 cm. The length is determined by aligning the zero of the vernier scale with one end of the object and the zero of the main scale with the other. The reading to the second decimal place is found by identifying the vernier mark that exactly aligns with a mark on the main scale. The total length is calculated using the main scale reading and the number of vernier divisions. Vernier scales are also found on instruments like barometers and spectrometers [19](#page=19).
#### 1.10.2 Micrometer screw gauge
A micrometer screw gauge measures very small lengths to an accuracy of 0.001 cm. It consists of a shaft scale and a rotating drum scale. One revolution of the drum moves the jaws by a precise amount, typically 0.5 mm. The drum scale is divided into 50 divisions, so each division represents a movement of $0.05 \text{ mm} / 50 = 0.001$ cm. A friction clutch ensures consistent force when gripping the object [20](#page=20).
> **Important:** Always check that a micrometer screw gauge reads zero when the jaws are closed. If not, the zero error must be accounted for in subsequent measurements [20](#page=20).
---
# Speed, velocity, and acceleration
This topic explores the fundamental concepts of motion, defining and distinguishing between speed, velocity, and acceleration, and detailing methods for their measurement and graphical representation.
## 2 Speed, velocity, and acceleration
Speed is defined as the distance traveled per unit of time. It quantifies how quickly an object is moving, irrespective of its direction. The average speed is calculated by dividing the total distance moved by the total time taken [22](#page=22).
The formula for average speed is:
$$ \text{Average speed} = \frac{\text{distance moved}}{\text{time taken}} $$ [22](#page=22).
To determine the instantaneous speed, one needs to consider the distance moved over a very short interval of time [22](#page=22).
### 2.1 Velocity
Velocity is similar to speed but includes the direction of motion. It is defined as the distance traveled per unit of time in a stated direction. Two objects moving at the same speed in opposite directions have different velocities. Speed is a scalar quantity, while velocity is a vector quantity [22](#page=22).
The formula for velocity is:
$$ \text{velocity} = \frac{\text{distance moved in a stated direction}}{\text{time taken}} $$ [22](#page=22).
Distance moved in a stated direction is also known as displacement, which is a vector quantity, unlike distance which is a scalar. Velocity can also be defined as [22](#page=22):
$$ \text{velocity} = \frac{\text{displacement}}{\text{time taken}} $$ [22](#page=22).
A body has uniform or constant velocity if it moves with a steady speed in a straight line. A curved path means the velocity is not uniform, even if the speed is constant. The units of speed and velocity are the same, such as kilometers per hour (km/h) or meters per second (m/s) [22](#page=22).
> **Tip:** While speed is just a magnitude, velocity has both magnitude and direction. For example, 20 m/s north is a velocity, whereas 20 m/s is a speed.
### 2.2 Acceleration
Acceleration is defined as the change of velocity per unit of time. When the velocity of a body changes, it is said to be accelerating [22](#page=22) [23](#page=23).
The formula for acceleration is:
$$ \text{acceleration} = \frac{\text{change of velocity}}{\text{time taken for change}} $$ [23](#page=23).
If a car starts from rest and reaches a velocity of 2 m/s due north after 1 second, its acceleration is 2 m/s per second due north, written as 2 m/s² [22](#page=22).
> **Example:** A car increases its speed from 20 m/s to 50 m/s in 5 seconds. Its acceleration is:
> $$ \text{acceleration} = \frac{(50 \text{ m/s} - 20 \text{ m/s})}{5 \text{ s}} = \frac{30 \text{ m/s}}{5 \text{ s}} = 6 \text{ m/s}^2 $$ [23](#page=23).
Acceleration is also a vector quantity, meaning both its magnitude and direction must be stated. However, when considering motion in a straight line, the magnitude of velocity equals speed, and the magnitude of acceleration equals the change of speed per unit time [23](#page=23).
A positive acceleration indicates an increasing velocity, while a negative acceleration (also called deceleration or retardation) indicates a decreasing velocity [23](#page=23).
> **Tip:** Uniform acceleration means the velocity changes by the same amount in equal time intervals.
### 2.3 Timers and motion analysis
Various devices are used in the laboratory to measure and analyze motion, including speed and acceleration [23](#page=23).
#### 2.3.1 Motion sensors
Motion sensors use ultrasonic echo techniques to determine an object's distance from the sensor. When connected to a datalogger and computer, they can directly plot distance–time graphs and, through further analysis, produce velocity–time graphs [23](#page=23).
#### 2.3.2 Tickertape timer
A tickertape timer uses a vibrating marker that makes dots on a paper tape pulled through it at regular intervals. A common timer makes 50 dots per second, meaning the interval between dots (a "tick") is 1/50 of a second. The distance between successive dots approximates the speed of the object pulling the tape. A "tentick" interval (1/5 second) is also frequently used [23](#page=23).
Tape charts are created by arranging successive tentick-length strips of tape side by side [23](#page=23).
* **Uniform speed** is represented by tape charts with equal distances moved in each tentick interval [23](#page=23).
* **Uniform acceleration** is shown by tape charts where each "step" (distance moved per tentick) is of equal size, indicating the speed increased by the same amount in every tentick interval [23](#page=23).
> **Example:** For a tape chart representing uniform acceleration, if the speed during the first tentick is 2 cm per 1/5 s (10 cm/s) and during the sixth tentick it is 12 cm per 1/5 s (60 cm/s), the average acceleration over the 1-second interval (5 tenticks) is:
> $$ \text{acceleration} = \frac{(60 \text{ cm/s} - 10 \text{ cm/s})}{1 \text{ s}} = 50 \text{ cm/s}^2 $$ [23](#page=23).
#### 2.3.3 Photogate timer
A photogate timer measures the time taken for an object with an "interrupt card" to pass through the gate. By knowing the length of the interrupt card, the velocity of the object can be calculated. Photogates are particularly useful for determining velocity at specific points [24](#page=24).
### 2.4 Practical work: Analyzing motion
Experiments involving pulling tape through a tickertape timer or using motion sensors allow for the analysis of personal motion and the motion of objects like trolleys on runways. By creating tape charts or obtaining distance–time and velocity–time graphs, one can identify periods of uniform speed, uniform acceleration, and changing acceleration [24](#page=24).
> **Tip:** When analyzing trolley motion down a runway with a tickertape timer, ignore the initial crowded dots, as they might not represent consistent motion. Focus on the later sections of the tape for analysis [24](#page=24).
### 2.5 Graphs of motion
* **Distance–time graphs:** These graphs plot the distance traveled against time. A straight, upward-sloping line indicates constant speed, while a steeper slope means higher speed. A horizontal line signifies the object is at rest [24](#page=24).
* **Velocity–time graphs:** These graphs plot velocity against time. A horizontal line indicates constant velocity (zero acceleration). An upward-sloping straight line represents uniform acceleration. The area under a velocity–time graph represents the displacement [24](#page=24).
> **Tip:** Understanding the relationship between the shape of a velocity-time graph and acceleration is crucial for problem-solving. A constant slope indicates constant acceleration.
---
# Force, momentum, and motion
This section explores the fundamental principles governing motion, including Newton's laws, the concepts of force, mass, inertia, and momentum, and the factors influencing acceleration, air resistance, and terminal velocity.
### 3.1 Falling bodies
In air, objects of different masses and shapes fall at different rates due to air resistance. However, in a vacuum, all objects fall at the same rate, regardless of their mass. This difference is attributed to air resistance having a greater proportional effect on lighter or less dense objects compared to heavier, denser ones. While a story suggests Galileo demonstrated this by dropping objects from the Leaning Tower of Pisa, it's now believed this specific experiment may be apocryphal [30](#page=30).
#### 3.1.1 Acceleration of free fall
When air resistance is negligible, all bodies falling freely under gravity accelerate uniformly. This constant acceleration is known as the **acceleration of free fall**, denoted by the symbol $g$. The value of $g$ varies slightly across the Earth but is constant at a specific location. For example, in India, it is approximately 9.8 m/s$^2$, often approximated as 10 m/s$^2$ for calculations. This means the velocity of a free-falling object increases by approximately 10 m/s every second [31](#page=31).
When using the equations of motion for free-falling bodies:
* For falling bodies, acceleration $a$ is positive, so $a = g = +10$ m/s$^2$ [31](#page=31).
* For rising bodies (which are decelerating), acceleration $a$ is negative, so $a = -g = -10$ m/s$^2$ [31](#page=31).
> **Tip:** When dealing with vertical motion involving gravity, always consider the direction of motion to assign the correct sign to acceleration $g$.
#### 3.1.2 Measuring $g$
The value of $g$ can be measured using an electronic timer and a falling object, such as a steel ball-bearing. An apparatus is set up where an electromagnet releases the ball, simultaneously starting a clock. When the ball hits an impact switch, the clock stops. The distance fallen ($s$), time taken ($t$), initial velocity ($u$), and acceleration ($a$) are related by the equation of motion $s = ut + \frac{1}{2}at^2$. For an object dropped from rest, $u = 0$ and $a = g$, so the equation becomes $s = \frac{1}{2}gt^2$. Rearranging this formula allows for the calculation of $g$ [31](#page=31):
$$ g = \frac{2s}{t^2} $$
Air resistance is considered negligible for dense objects falling short distances in such experiments [31](#page=31).
#### 3.1.3 Worked example: Vertical projection
Consider a ball projected vertically upwards with an initial velocity ($u$) of 30 m/s. We neglect air resistance and take $g = 10$ m/s$^2$.
* **a) Maximum height:** At its maximum height, the ball's velocity ($v$) is momentarily 0 m/s. We use the equation $v^2 = u^2 + 2as$ [32](#page=32).
Here, $u = 30$ m/s, $a = -10$ m/s$^2$ (since it's decelerating), and $v = 0$ m/s.
$$ 0^2 = (30 \text{ m/s})^2 + 2(-10 \text{ m/s}^2) \times s $$
$$ 0 = 900 \text{ m}^2/\text{s}^2 - 20 \text{ m/s}^2 \times s $$
$$ 20 \text{ m/s}^2 \times s = 900 \text{ m}^2/\text{s}^2 $$
$$ s = \frac{900 \text{ m}^2/\text{s}^2}{20 \text{ m/s}^2} = 45 \text{ m} $$
The maximum height reached is 45 meters [32](#page=32).
* **b) Time to return to starting point:** Let $t$ be the time to reach the highest point. We use the equation $v = u + at$.
$$ 0 \text{ m/s} = 30 \text{ m/s} + (-10 \text{ m/s}^2) \times t $$
$$ -30 \text{ m/s} = -10 \text{ m/s}^2 \times t $$
$$ t = \frac{-30 \text{ m/s}}{-10 \text{ m/s}^2} = 3 \text{ s} $$
The time taken to reach the highest point is 3 seconds. The downward journey takes the same amount of time, so the total time to return to the starting point is $3 \text{ s} + 3 \text{ s} = 6 \text{ s}$ [32](#page=32).
#### 3.1.4 Distance–time graphs
For a body falling freely from rest, the distance ($s$) covered is related to time ($t$) by $s = \frac{1}{2}gt^2$. A graph of distance ($s$) against time ($t$) will be a curve. However, a graph of distance ($s$) against the square of time ($t^2$) will be a straight line passing through the origin, as $s$ is directly proportional to $t^2$ when $g$ is constant [32](#page=32).
> **Tip:** The shape of a distance-time graph can tell you about the object's motion. A straight line indicates constant velocity, while a curve indicates acceleration.
#### 3.1.5 Projectiles
The motion of a projectile can be understood by considering its horizontal and vertical components independently. The vertical motion of a projectile is governed by gravity, just like a freely falling object. The horizontal velocity of a projectile does not affect its vertical acceleration [32](#page=32).
* **Horizontal and Vertical Motion Independence:** If a ball is thrown horizontally from a cliff and takes 3 seconds to reach the ground, its height can be calculated using the vertical motion only. With an initial vertical velocity ($u$) of 0 m/s, acceleration ($a$) of $g = +10$ m/s$^2$, and time ($t$) of 3 s, the height ($s$) is [33](#page=33):
$$ s = ut + \frac{1}{2}at^2 $$
$$ s = (0 \text{ m/s})(3 \text{ s}) + \frac{1}{2}(10 \text{ m/s}^2)(3 \text{ s})^2 $$
$$ s = 0 + \frac{1}{2}(10 \text{ m/s}^2)(9 \text{ s}^2) = 45 \text{ m} $$
The height of the cliff is 45 meters [33](#page=33).
* **Range of Projectiles:** For projectiles launched near ground level at an angle (e.g., cricket balls), the horizontal distance traveled (range) depends on two factors:
1. **Speed of projection:** A higher initial speed leads to a greater range [33](#page=33).
2. **Angle of projection:** Neglecting air resistance, the range is maximized when the angle of projection is 45 degrees [33](#page=33).
### 3.2 Newton's laws of motion
*Note: While the provided pages focus on falling bodies and related concepts, Newton's laws are foundational to these principles. Based on common physics curricula and the context of "force, momentum, and motion," these laws are typically introduced here.*
Newton's laws of motion describe the relationship between an object's motion and the forces acting upon it.
#### 3.2.1 Newton's first law of motion (law of inertia)
An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force [PAGE NUMBER NEEDED. This property is known as inertia. Inertia is a measure of an object's resistance to changes in its state of motion and is directly proportional to its mass.
#### 3.2.2 Newton's second law of motion
Newton's second law states that the acceleration ($a$) of an object is directly proportional to the net force ($F$) acting on it and inversely proportional to its mass ($m$). This relationship is expressed by the formula:
$$ F = ma $$
The unit of force is the Newton (N), defined as the force required to accelerate a 1-kilogram mass at 1 meter per second squared.
#### 3.2.3 Newton's third law of motion
For every action, there is an equal and opposite reaction. This means that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These forces act on different objects and do not cancel each other out.
### 3.3 Momentum
Momentum ($p$) is a measure of an object's motion and is defined as the product of its mass ($m$) and its velocity ($v$):
$$ p = mv $$
Momentum is a vector quantity, meaning it has both magnitude and direction. The SI unit of momentum is kilogram-meter per second (kg m/s) [PAGE NUMBER NEEDED.
#### 3.3.1 Principle of conservation of momentum
In the absence of external forces, the total momentum of a system remains constant [PAGE NUMBER NEEDED. This principle is fundamental and applies to collisions and explosions.
### 3.4 Air resistance and terminal velocity
Air resistance is a type of friction that opposes the motion of an object through the air. Its magnitude depends on factors such as the object's speed, shape, and surface area [30](#page=30).
**Terminal velocity** is reached when the force of air resistance acting on a falling object becomes equal in magnitude to the object's weight [PAGE NUMBER NEEDED. At this point, the net force on the object is zero, and it stops accelerating, falling at a constant velocity [PAGE NUMBER NEEDED. Objects with larger surface areas or lower masses tend to have lower terminal velocities because air resistance has a greater effect on them relative to their weight [30](#page=30).
> **Example:** A parachute is designed to increase air resistance by providing a large surface area, thereby lowering the skydiver's terminal velocity to a safe landing speed.
---
# Energy and its transformations
This section explores the concept of energy, its various forms, how it is transferred, and the fundamental principle of its conservation.
### 4.1 Forces and turning effects
#### 4.1.1 Moment of a force
The turning effect of a force is known as the moment of a force. It is calculated by multiplying the applied force by the perpendicular distance of the line of action of the force from the pivot or fulcrum. The unit for the moment of a force is the newton metre (N m) [52](#page=52).
The formula for the moment of a force is:
$$ \text{Moment} = \text{Force} \times \text{perpendicular distance from fulcrum} $$ [52](#page=52).
The position of a force relative to a pivot significantly affects its turning effect. For instance, applying a force at the edge of a door (further from the hinge) creates a larger moment than applying it closer to the hinge [52](#page=52).
> **Tip:** To maximize the turning effect, apply the force as far as possible from the pivot.
#### 4.1.2 Balancing a beam
A beam can be balanced on a pivot when the sum of the clockwise turning effects equals the sum of the anticlockwise turning effects. This state is known as equilibrium, where the net moment on the beam is zero. If a beam tends to swing in one direction, adjustments can be made by moving the applied forces or weights further from or nearer to the pivot to alter their moments [52](#page=52).
#### 4.1.3 The law of moments
The law of moments states that for a body to be in equilibrium, the sum of the clockwise moments about any point must equal the sum of the anticlockwise moments about the same point. This implies that there is no net moment acting on a body in equilibrium [53](#page=53).
**Worked Example:**
Consider a see-saw with individuals of different weights at various positions. To find an unknown weight ($W$), moments are taken about the fulcrum. The anticlockwise moment is calculated by summing the products of weights and their distances from the fulcrum. The clockwise moment is similarly calculated. By equating these two moments according to the law of moments, the unknown weight can be determined [53](#page=53).
#### 4.1.4 Levers
A lever is a device that can rotate around a pivot. In a working lever, an effort force is used to overcome a resisting force called the load, with the pivot point being the fulcrum. Examples of levers include crowbars, wheelbarrows, scissors, and spanners. The effort required to move a load depends on the distances from the fulcrum, as governed by the law of moments [53](#page=53).
#### 4.1.5 Conditions for equilibrium
For a body to be in equilibrium, two conditions must be met:
1. The sum of forces acting in one direction must equal the sum of forces acting in the opposite direction. This means there is no resultant force [54](#page=54).
2. The law of moments must apply, meaning the sum of clockwise moments equals the sum of anticlockwise moments about any point. This means there is no resultant turning effect [54](#page=54).
A body in equilibrium experiences no net force and no net turning effect [54](#page=54).
**Example:**
Consider a heavy plank resting on two trestles. The total upward forces (reactions) from the trestles must equal the downward weight of the plank. By taking moments about one of the trestles, the forces exerted by each trestle can be calculated [54](#page=54).
### 4.2 Centres of mass
#### 4.2.1 Definition and behavior
A body can be considered to have its entire mass concentrated at a single point, known as its centre of mass or centre of gravity. The weight of an object can be treated as acting at this point. For regularly shaped objects with uniform density, the centre of mass is at their geometric center [56](#page=56).
#### 4.2.2 Stability and toppling
The position of an object's centre of mass significantly influences its stability. A body will topple if the vertical line passing through its centre of mass falls outside its base of support. Conversely, if this line remains within the base, the body will be stable and will not topple [56](#page=56) [57](#page=57).
> **Tip:** To increase the stability of an object, lower its centre of mass and widen its base of support.
The stability of an object can be enhanced by:
* Lowering its centre of mass [57](#page=57).
* Increasing the area of its base [57](#page=57).
This principle is crucial in the design of vehicles, such as tractors and double-decker buses, to prevent overturning. Racing cars, for instance, have low centres of mass and wide wheelbases for maximum stability [57](#page=57).
#### 4.2.3 States of equilibrium
There are three states of equilibrium:
a) **Stable equilibrium:** If a body is slightly displaced and then released, it returns to its original position. Its centre of mass rises when displaced. An example is a ball at the bottom of a dish [58](#page=58).
b) **Unstable equilibrium:** If a body is slightly displaced and then released, it moves further away from its original position. Its centre of mass falls when displaced, creating a moment that increases the displacement. A balanced ruler on its edge is an example [58](#page=58).
c) **Neutral equilibrium:** If a body is displaced, it remains in its new position. Its centre of mass neither rises nor falls. An example is a ball on a flat surface [58](#page=58).
#### 4.2.4 Practical applications
Many balancing tricks and toys rely on positioning the centre of mass correctly for stability. Self-righting toys, for example, have a heavy base, ensuring that when tilted, the weight acting through the centre of mass creates a moment that restores the toy to its upright position [58](#page=58) [59](#page=59).
### 4.3 Circular motion and satellites
#### 4.3.1 Orbital motion
An object in orbit, such as a satellite around the Earth, is continuously pulled towards the central body by gravity. If the object's tangential velocity is sufficient, it will follow a path where its forward motion balances the inward pull of gravity, resulting in a stable orbit. This is similar to how a projectile can achieve orbit if fired with enough speed [50](#page=50).
The orbital period ($T$) of a satellite is the time it takes to complete one orbit. For a circular orbit, the velocity ($v$) is related to the orbital radius ($r$) and period by the formula $v = \frac{2\pi r}{T}$. Satellites in higher orbits have longer orbital periods than those in lower orbits [50](#page=50).
#### 4.3.2 Types of satellites
* **Communication satellites:** These are often placed in geostationary orbits above the equator, approximately 36,000 km high. They orbit at the same speed as the Earth rotates, appearing stationary from the Earth's surface with an orbital period of 24 hours. They are used for transmitting television, telephone, and data signals. Mobile phone networks utilize satellites in lower equatorial orbits that require regular adjustments to counteract atmospheric drag [50](#page=50).
* **Monitoring satellites:** These satellites orbit the Earth rapidly in low polar orbits, passing over both poles. At a height of 850 km, their orbital period is about 100 minutes. As the Earth rotates beneath them, they scan the entire surface, making them useful for mapping and monitoring, particularly for weather forecasting by transmitting infrared images of cloud patterns [50](#page=50).
#### 4.3.3 Centripetal force
Circular motion requires an unbalanced force acting towards the center of the circle, known as the centripetal force. For a car rounding a bend, friction between the tires and the road provides this centripetal force. A larger centripetal force is required if the car travels faster, the bend is more curved, or the car has more mass (e.g., more passengers). Racing car tires, like "slicks" on dry tracks, are designed to maximize this friction for better grip during cornering [51](#page=51).
### 4.4 Energy and its transformations (General Introduction - Not extensively covered in pages 50-59 but implied by context)
While the provided pages focus on mechanics like moments, levers, and circular motion, the broader topic of "Energy and its transformations" encompasses the fundamental concept of energy as the capacity to do work. Energy exists in various forms, including kinetic energy (energy of motion), potential energy (stored energy due to position or state), thermal energy, chemical energy, and radiant energy. The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between systems [implied from general physics principles.
For instance, in circular motion, the kinetic energy of a satellite is maintained by the continuous work done by the gravitational force (though the force itself does no net work in a circular orbit as it is perpendicular to the velocity) [implied from general physics principles. In levers, the effort force applied over a distance does work to overcome the load [53](#page=53).
#### 4.4.1 Kinetic energy
Kinetic energy is the energy an object possesses due to its motion. The faster an object moves, the greater its kinetic energy.
#### 4.4.2 Potential energy
Potential energy is stored energy. Gravitational potential energy is energy stored by an object due to its position in a gravitational field. For example, a book held at a height has gravitational potential energy.
#### 4.4.3 Power
Power is the rate at which work is done or energy is transferred. It is measured in watts (W). A more powerful engine can do more work in the same amount of time, or the same amount of work in less time.
#### 4.4.4 Driving and car safety
Concepts related to energy and forces are directly applicable to driving and car safety.
* **Kinetic energy and braking:** The kinetic energy of a moving car increases with the square of its speed ($KE = \frac{1}{2}mv^2$). This means that doubling the speed quadruples the kinetic energy, requiring four times the braking distance to dissipate that energy as heat through friction in the brakes [implied from general physics principles.
* **Centripetal force and cornering:** As discussed, the centripetal force is essential for a car to turn. If the required centripetal force exceeds the maximum friction available, the car will skid [51](#page=51).
* **Work done by seatbelts and airbags:** In a collision, seatbelts and airbags work by increasing the time over which the driver's momentum changes, thereby reducing the force exerted on the driver, as force is the rate of change of momentum ($F = \frac{\Delta p}{\Delta t}$). This minimizes injury by reducing the impact force, which is related to the work done to stop the occupant [implied from general physics principles.
* **Crumple zones:** Modern cars incorporate crumple zones designed to deform upon impact. This deformation absorbs a significant amount of kinetic energy, reducing the force transmitted to the occupants and thus enhancing safety [implied from general physics principles.
---
# Electricity and magnetism
Electricity and magnetism is a foundational area of physics that explains the behavior of electric charges, currents, and magnetic fields, and their interconnectedness.
## 5. Electricity and magnetism
### 5.1 Static electricity
Static electricity involves the accumulation of electric charge on the surface of an object. This can occur through friction, contact, or induction. When objects with different properties are rubbed together, electrons can be transferred, leaving one object positively charged and the other negatively charged .
#### 5.1.1 Charging by friction
Friction between two insulators can lead to a transfer of electrons. For example, rubbing a balloon on hair causes electrons to move from the hair to the balloon, making the balloon negatively charged and the hair positively charged .
#### 5.1.2 Charging by contact and induction
An object can become charged by touching a charged object (charging by contact) or by the influence of a nearby charged object without direct contact (charging by induction) .
#### 5.1.3 Uses of static electricity
Static electricity has several practical applications:
* **Flue-ash precipitation:** Electrostatic precipitators use charged plates to remove ash particles from industrial chimneys .
* **Photocopiers:** These devices use static electricity to transfer toner powder onto paper to create copies .
* **Inkjet printers:** Charged ink droplets are deflected by electric fields to create images on paper .
* **Van de Graaff generator:** This device produces a continuous supply of high voltage static electricity, used for demonstrations and experiments .
### 5.2 Electric current
An electric current is the flow of electric charge. In metals, this flow is primarily due to electrons moving from the negative to the positive terminal of a battery in a circuit .
#### 5.2.1 Direct and alternating current
* **Direct Current (DC):** The flow of charge is in one direction only. Batteries typically provide DC .
* **Alternating Current (AC):** The direction of charge flow periodically reverses. Household electricity supply is AC, with a frequency of typically 50 Hz or 60 Hz .
#### 5.2.2 Measuring electric current
Electric current is measured in amperes (A) using an ammeter, which is connected in series with the circuit component being measured .
#### 5.2.3 Relationship between charge and current
The quantity of charge ($Q$) is related to the current ($I$) and the time ($t$) by the formula $Q = It$ .
### 5.3 Potential difference
Potential difference (p.d.), also known as voltage, is the energy transferred per unit charge between two points in a circuit. It is measured in volts (V) using a voltmeter, which is connected in parallel across the component where the p.d. is being measured .
#### 5.3.1 Voltages in series and parallel circuits
* **Series circuits:** The total voltage across components in series is the sum of the voltages across each component. For example, if $V$ is the supply voltage and $V_1, V_2, V_3$ are voltages across components, then $V = V_1 + V_2 + V_3$ .
* **Parallel circuits:** The voltage across components connected in parallel is the same. So, if $V_1$ and $V_2$ are voltages across two parallel components, $V_1 = V_2$ .
#### 5.3.2 Potential divider
A potential divider circuit uses two or more resistors in series to provide a specific fraction of the total supply voltage. For two resistors $R_1$ and $R_2$ in series with a supply voltage $V$, the voltage across $R_1$ is $V_1 = V \frac{R_1}{R_1 + R_2}$ and the voltage across $R_2$ is $V_2 = V \frac{R_2}{R_1 + R_2}$ .
### 5.4 Resistance
Resistance ($R$) is a measure of how difficult it is for electric current to flow through a material. It is defined by Ohm's law, which states that the current ($I$) through a conductor is directly proportional to the potential difference ($V$) across it, provided all physical conditions remain unchanged: $V = IR$. Resistance is measured in ohms ($\Omega$) .
#### 5.4.1 Factors affecting resistance
The resistance of a conductor depends on:
* **Length ($l$):** Resistance is directly proportional to length .
* **Cross-sectional area ($A$):** Resistance is inversely proportional to cross-sectional area .
* **Resistivity ($\rho$):** An intrinsic property of the material, representing its resistance per unit length and unit cross-sectional area. The formula is $R = \frac{\rho l}{A}$ .
* **Temperature:** For most conductors, resistance increases with temperature.
#### 5.4.2 Resistance in series and parallel
* **Series circuits:** The total resistance is the sum of individual resistances: $R_{total} = R_1 + R_2 + R_3 + \dots$ .
* **Parallel circuits:** The reciprocal of the total resistance is the sum of the reciprocals of individual resistances: $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots$ .
### 5.5 Capacitors
Capacitors store electrical energy in an electric field. They typically consist of two conductive plates separated by a dielectric material. The capacitance ($C$) is defined as the ratio of the charge ($Q$) stored on one plate to the potential difference ($V$) between the plates: $C = \frac{Q}{V}$ [No page available for direct definition, but implied by context of electronic systems. Capacitance is measured in farads (F).
### 5.6 Electric power
Electric power ($P$) is the rate at which electrical energy is transferred or converted. It can be calculated using the following formulas:
* $P = VI$ (Power equals voltage times current) .
* $P = I^2R$ (Power equals current squared times resistance) .
* $P = \frac{V^2}{R}$ (Power equals voltage squared divided by resistance) .
Power is measured in watts (W), where 1 watt is equal to 1 joule per second. Household electricity meters, like joulemeters, measure the total electrical energy consumed in joules .
#### 5.6.1 Household circuits
Household electrical systems are typically wired in parallel to ensure each appliance receives the full mains voltage (e.g., 230 V in the UK) and can be operated independently. Switches and fuses are always placed in the live wire for safety .
### 5.7 Electronic systems
Electronic systems use components like semiconductors to control the flow of electricity. They often involve transducers that convert physical quantities into electrical signals (input transducers) or electrical signals into physical quantities (output transducers).
#### 5.7.1 Input transducers
* **Light-dependent resistor (LDR):** Its resistance decreases as light intensity increases, making it useful for light-sensitive circuits .
* **Thermistor:** Its resistance changes significantly with temperature, typically decreasing as temperature rises. This is useful for temperature sensing and control .
#### 5.7.2 Output transducers
* **Relays:** Electrically operated switches that allow a small current in one circuit to control a larger current in another circuit .
* **Transistors:** Semiconductor devices used as switches or amplifiers in electronic circuits. They are crucial for miniaturization and efficiency in modern electronics .
#### 5.7.3 Applications of electronic systems
Electronic systems are prevalent in homes (washing machines, alarms), industry (robots, automation), and medicine (scanners, pacemakers) due to their compactness, reliability, speed, and low energy consumption .
### 5.8 Electromagnetic effects
Electromagnetism is the study of the relationship between electricity and magnetism. Electric currents create magnetic fields, and changing magnetic fields can induce electric currents.
#### 5.8.1 Electromagnets
An electromagnet is created when an electric current flows through a coil of wire, often wrapped around a ferromagnetic core. The strength of an electromagnet can be increased by increasing the current, the number of turns in the coil, or the permeability of the core .
* **Field due to a straight wire:** A current-carrying wire produces a magnetic field in concentric circles around it. The direction of the field can be determined by the right-hand screw rule .
* **Oersted's discovery:** In 1819, Hans Christian Ørsted discovered that an electric current produces a magnetic effect .
#### 5.8.2 Electric motors
Electric motors convert electrical energy into mechanical energy. They operate on the principle that a current-carrying conductor placed in a magnetic field experiences a force [No specific page for motors, but implied by topic.
#### 5.8.3 Generators
Generators convert mechanical energy into electrical energy using the principle of electromagnetic induction. A changing magnetic field induces an electromotive force (e.m.f.) or voltage in a conductor .
* **Alternators:** Produce alternating current (AC). They are commonly used in power stations and cars .
* **Dynamos:** Produce direct current (DC).
* **Bicycle generators:** Use a rotating magnet to induce voltage in a stationary coil .
#### 5.8.4 Transformers
Transformers are devices used to increase or decrease alternating voltages. They consist of two coils wound around a common iron core. The ratio of the voltages across the coils is equal to the ratio of the number of turns in the coils ($ \frac{V_s}{V_p} = \frac{N_s}{N_p} $) .
* **Step-up transformer:** Increases voltage.
* **Step-down transformer:** Decreases voltage.
Transformers are essential for the efficient transmission of electrical power over long distances via the National Grid, where voltages are stepped up for transmission and then stepped down for distribution. Eddy currents induced in the core can cause heating, which is reduced by using laminated cores .
#### 5.8.5 Electromagnetic induction applications
* **Moving-coil microphone:** Sound waves vibrate a coil in a magnetic field, inducing a current .
* **Magnetic recording:** Varying magnetization on tapes or disks induces electrical signals .
#### 5.8.6 Electric meters
Electric meters measure electrical quantities. For example, an electric meter in a household measures the total electrical energy consumed. Ammeters measure current, and voltmeters measure potential difference .
---
## Common mistakes to avoid
- Review all topics thoroughly before exams
- Pay attention to formulas and key definitions
- Practice with examples provided in each section
- Don't memorize without understanding the underlying concepts
Glossary
| Term | Definition |
|---|---|
| Standard notation | A method for writing numbers, particularly very large or very small ones, in the form $a \times 10^n$, where $1 \le a < 10$ and $n$ is an integer. |
| Significant figures | The number of digits in a measured value that are known with some degree of certainty, indicating the precision of the measurement. |
| Parallax error | An apparent shift in the position of an object when viewed from different angles, often occurring when reading scales on measuring instruments. |
| Systematic error | An error that consistently affects measurements in the same way, often due to faulty equipment or a flawed experimental method. |
| Vernier scale | A secondary, sliding scale used with a main scale to achieve more precise readings, typically to a fraction of the smallest division on the main scale. |
| Micrometer screw gauge | A precision measuring instrument used for making very accurate measurements of small lengths or thicknesses, typically to three decimal places of a centimetre. |
| Speed | The distance traveled per unit of time; it is a scalar quantity. |
| Velocity | The rate of change of displacement; it is a vector quantity, meaning it has both magnitude (speed) and direction. |
| Acceleration | The rate of change of velocity; it is a vector quantity. |
| Tickertape timer | A device used to analyze motion by recording short time intervals at regular intervals on a paper tape pulled through it. |
| Photogate timer | An electronic device that measures the time taken for an object with an interrupt card to pass through a light beam. |
| Motion sensor | A device that uses techniques like ultrasonic echoes to determine the position of an object and can be used with a datalogger to plot distance-time or velocity-time graphs. |
| Velocity–time graph | A graph where velocity is plotted against time. The gradient of the graph represents acceleration, and the area under the graph represents distance traveled. |
| Distance–time graph | A graph where distance is plotted against time. The gradient of the graph represents velocity. |
| Equations of motion | A set of kinematic equations that describe the motion of objects with uniform acceleration, typically relating displacement, initial velocity, final velocity, acceleration, and time. |
| Acceleration of free fall (g) | The constant acceleration experienced by an object falling freely under gravity, approximately $9.8 \, \text{m/s}^2$ near the Earth's surface. |
| Projectiles | Objects moving under the influence of gravity, where their horizontal and vertical motions can be analyzed independently. |
| Density | Mass per unit volume of a substance, calculated as $\rho = m/V$. |
| Floating and sinking | An object floats if its density is less than the density of the fluid it is in; it sinks if its density is greater. |
| Force | A push or a pull that can cause a change in motion, speed, direction, or shape of an object. |
| Weight | The force of gravity acting on an object; it is a vector quantity and depends on the gravitational field strength. |
| Newton | The SI unit of force. |
| Hooke’s law | States that the extension of a spring or elastic material is directly proportional to the stretching force applied, provided the elastic limit is not exceeded ($F = kx$). |
| Moment of a force | The turning effect of a force about a pivot, calculated as force × perpendicular distance from the pivot. Measured in newton-metres (N m). |
| Law of moments | States that for a body in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point. |
| Levers | Simple machines consisting of a rigid bar that turns about a fixed point (fulcrum), used to overcome a load with an effort. |
| Conditions for equilibrium | For a body to be in equilibrium, the vector sum of all forces acting on it must be zero, and the sum of all moments about any point must also be zero. |
| Centre of mass | The single point where the entire weight of an object can be considered to act; it affects an object's stability. |
| Stability | The ability of an object to return to its original position after being slightly displaced. Affected by the position of the center of mass and the base of support. |
| States of equilibrium | Stable (returns to original position), unstable (moves further away), and neutral (stays in new position). |
| Momentum | The product of an object's mass and its velocity ($p = mv$); it is a vector quantity. |
| Conservation of momentum | The principle that the total momentum of a system remains constant if no external forces act on it. |
| Impulse | The product of force and the time for which it acts ($Ft$), equal to the change in momentum. |
| Energy transfer | The movement of energy from one form to another or from one object to another. |
| Forms of energy | Chemical, potential (gravitational and strain), kinetic, electrical, heat, light, sound, nuclear. |
| Work | Done when a force moves an object in the direction of the force; measured in joules ($W = Fd$). |
| Power | The rate at which work is done or energy is transferred ($P = E/t$); measured in watts (W). |
| Efficiency | The ratio of useful energy output to total energy input, often expressed as a percentage. |
| Kinetic energy (k.e.) | The energy an object possesses due to its motion ($E_k = \frac{1}{2}mv^2$). |
| Potential energy (p.e.) | The energy an object possesses due to its position or condition. Gravitational potential energy ($E_p = mgh$) and strain energy are common forms. |
| Conservation of energy | The principle that energy cannot be created or destroyed, only transferred or transformed from one form to another. |
| Specific heat capacity | The amount of heat energy required to raise the temperature of 1 kg of a substance by 1 °C ($Q = mc\Delta\theta$). |
| Thermal capacity | The amount of heat energy required to raise the temperature of an entire body by 1 °C (thermal capacity = mass × specific heat capacity). |
| Specific latent heat | The amount of heat energy required to change the state of 1 kg of a substance without changing its temperature (fusion: $Q = ml_f$; vaporisation: $Q = ml_v$). |
| Melting point | The fixed temperature at which a solid changes into a liquid. |
| Boiling point | The fixed temperature at which a liquid changes into a gas at a given pressure. |
| Evaporation | The process by which molecules escape from the surface of a liquid at any temperature. |
| Boiling | The process by which a liquid changes into a gas at a specific temperature, with the formation of bubbles within the liquid. |
| Conduction | Heat transfer through matter by the vibration of particles, without the overall movement of the matter itself. |
| Convection | Heat transfer through fluids (liquids or gases) by the movement of the heated fluid itself, creating convection currents. |
| Radiation | Heat transfer through electromagnetic waves, which can travel through a vacuum. |
| Vacuum flask | A container designed to minimize heat transfer by conduction, convection, and radiation, using vacuum insulation and silvered surfaces. |
| Greenhouse effect | The process by which certain gases in the atmosphere trap heat radiation, leading to warming. |
| Wavefronts | Lines connecting points on a wave that are in the same phase. |
| Rays | Lines drawn perpendicular to wavefronts, indicating the direction of wave propagation. |
| Reflection | The bouncing back of waves from a surface, where the angle of incidence equals the angle of reflection. |
| Refraction | The bending of waves as they pass from one medium to another, caused by a change in speed. |
| Diffraction | The spreading of waves as they pass through a gap or around an obstacle. |
| Interference | The effect produced when two or more waves superpose, resulting in larger or smaller amplitudes depending on whether they are in phase or out of phase. |
| Polarisation | An effect that occurs only with transverse waves, describing the orientation of the oscillations. |
| Sources of light | Luminous (emit their own light) and non-luminous (reflect light). |
| Laser | A device that produces a narrow, highly concentrated beam of light through stimulated emission. |
| Shadows | Areas where light is blocked by an opaque object, consisting of an umbra (total shadow) and penumbra (partial shadow). |
| Speed of light | The constant speed at which light travels in a vacuum, approximately $3 \times 10^8 \, \text{m/s}$. |
| Law of reflection | States that the angle of incidence equals the angle of reflection, and the incident ray, reflected ray, and normal all lie in the same plane. |
| Periscopes | Optical instruments that use mirrors or prisms to allow observation over or around obstacles. |
| Regular reflection | Reflection of light from a smooth surface, where parallel incident rays are reflected as parallel rays. |
| Diffuse reflection | Reflection of light from a rough surface, where parallel incident rays are scattered in many directions. |
| Lateral inversion | The apparent left-right reversal of an image formed by a plane mirror. |
| Real image | An image formed by actual rays of light converging at a point, which can be projected onto a screen. |
| Virtual image | An image formed by apparent rays of light diverging from a point, which cannot be projected onto a screen. |
| Refraction of light | The bending of light rays as they pass from one medium to another due to a change in speed. |
| Normal | A line drawn perpendicular to a surface at the point where a ray strikes it. |
| Optically denser medium | A medium in which light travels slower than in another medium. |
| Refractive index (n) | The ratio of the speed of light in a vacuum to the speed of light in a medium ($n = c/v$), or the ratio of the sine of the angle of incidence to the sine of the angle of refraction ($n = \sin i / \sin r$). |
| Dispersion | The splitting of white light into its constituent colors when passing through a prism, due to different refractive indices for different colors. |
| Spectrum | The range of colors produced when white light is dispersed. |
| Total internal reflection | The phenomenon where light traveling from a denser to a less dense medium is completely reflected back into the denser medium when the angle of incidence exceeds the critical angle. |
| Critical angle (c) | The angle of incidence in a denser medium for which the angle of refraction in a less dense medium is 90°. |
| Light pipes and optical fibres | Devices that transmit light along curved paths using total internal reflection. |
| Lenses | Transparent optical components, usually made of glass or plastic, with at least one curved surface, used to converge or diverge light. |
| Converging (convex) lens | A lens that is thicker in the center and converges parallel rays of light to a focal point. |
| Diverging (concave) lens | A lens that is thinner in the center and diverges parallel rays of light as if they originated from a focal point. |
| Principal axis | The line passing through the optical center of a lens and perpendicular to its surfaces. |
| Optical centre (C) | The central point of a lens through which rays of light pass undeviated (for thin lenses). |
| Principal focus (F) | The point on the principal axis where parallel rays of light converge (converging lens) or appear to diverge from (diverging lens) after passing through the lens. |
| Focal length (f) | The distance from the optical center of a lens to its principal focus. |
| Ray diagrams | Diagrams used to show the path of light rays through optical systems to determine the position, nature, and size of images. |
| Magnification (m) | The ratio of the image height to the object height, or the ratio of the image distance to the object distance ($m = h_i/h_o = v/u$). |
| Power of a lens | The reciprocal of its focal length in meters ($P = 1/f$), measured in dioptres (D). |
| Magnifying glass | A converging lens used to produce a magnified, upright, virtual image of an object placed within its focal length. |
| Spectacles | Lenses worn to correct vision defects like short sight and long sight. |
| Short sight (myopia) | A condition where distant objects appear blurred because the eye focuses light in front of the retina. Corrected with diverging lenses. |
| Long sight (hyperopia) | A condition where close objects appear blurred because the eye focuses light behind the retina. Corrected with converging lenses. |
| Electromagnetic radiation | Energy that travels as transverse waves, comprising a spectrum of different wavelengths and frequencies, including light, radio waves, microwaves, infrared, ultraviolet, X-rays, and gamma rays. |
| Photoelectric effect | The emission of electrons from a material when electromagnetic radiation of sufficient frequency falls on it. |
| Photons | Packets of energy associated with electromagnetic radiation, whose energy is proportional to their frequency ($E = hf$). |
| Waves or particles | Electromagnetic radiation exhibits both wave-like (interference, diffraction) and particle-like (photoelectric effect) properties. |
| Sound waves | Longitudinal waves produced by vibrations, which travel through a medium by compressions and rarefactions. |
| Longitudinal waves | Waves in which the particles of the medium vibrate parallel to the direction of wave propagation. |
| Compressions | Regions in a longitudinal wave where particles are closest together. |
| Rarefactions | Regions in a longitudinal wave where particles are farthest apart. |
| Reflection of sound | The bouncing of sound waves off a surface, creating an echo. |
| Speed of sound | The speed at which sound travels through a medium, dependent on the medium's properties (e.g., temperature, density). |
| Limits of audibility | The range of frequencies that can be heard by the human ear, typically from about 20 Hz to 20,000 Hz. |
| Pitch of a note | Determined by the frequency of the sound wave; higher frequency means higher pitch. |
| Loudness | Determined by the amplitude of the sound wave; larger amplitude means greater loudness. |
| Quality (timbre) | The characteristic sound of an instrument, determined by the mixture of fundamental frequency and overtones. |
| Ultrasonics | Sound waves with frequencies above the upper limit of human hearing (typically above 20 kHz). |
| Seismic waves | Waves produced by earthquakes, including longitudinal (P-waves) and transverse (S-waves) waves. |
| Magnetic fields | The region around a magnet or current-carrying conductor where magnetic forces are exerted. Represented by lines of force. |
| Magnetic poles | Regions of a magnet where the magnetic force is strongest, typically near the ends (North and South poles). |
| Law of magnetic poles | Like poles repel, unlike poles attract. |
| Magnetisation | The process of making a magnetic material magnetic, either temporarily (soft iron) or permanently (steel). |
| Soft magnetic materials | Materials that are easily magnetized and demagnetized, used in electromagnets. |
| Hard magnetic materials | Materials that are difficult to magnetize but retain their magnetism, used for permanent magnets. |
| Solenoid | A coil of wire wound into a cylindrical shape, producing a magnetic field similar to that of a bar magnet. |
| Right-hand screw rule | A rule relating the direction of current in a straight wire or solenoid to the direction of the magnetic field it produces. |
| Electromagnets | Magnets created by passing an electric current through a coil of wire, often wound around a soft iron core. Their strength can be varied. |
| Electric bells | Devices that use electromagnets to create a vibrating hammer that strikes a gong repeatedly. |
| Relays | Electrically operated switches used to control a second circuit, often with a higher current or voltage, using a low-power signal. |
| Reed switches | Switches activated by a magnetic field, often used in alarms or as relays. |
| Circuit breakers | Safety devices that automatically interrupt an electric circuit when the current becomes dangerously high, acting as resettable fuses. |
| Telephone | A communication device that converts sound into electrical signals (microphone) and electrical signals back into sound (receiver), often using carbon microphones and electromagnets. |
| Electric current | The flow of electric charge, typically electrons in metals. Measured in amperes (A). |
| Ampere (A) | The SI unit of electric current. |
| Coulomb (C) | The SI unit of electric charge ($1 \, \text{C} = 1 \, \text{A} \cdot \text{s}$). |
| Circuit diagrams | Symbolic representations of electrical circuits using standard symbols for components like batteries, resistors, lamps, switches, ammeters, and voltmeters. |
| Series circuit | Components connected end-to-end, so the same current flows through each. |
| Parallel circuit | Components connected side-by-side, providing multiple paths for the current. |
| Direct current (d.c.) | Electric current that flows in one direction only. |
| Alternating current (a.c.) | Electric current that periodically reverses direction. |
| Hertz (Hz) | The SI unit of frequency, equal to one cycle per second. |
| Potential difference (p.d.) | The work done per unit charge in moving charge between two points in an electric field. Also called voltage. |
| Volt (V) | The SI unit of potential difference and electromotive force ($1 \, \text{V} = 1 \, \text{J/C}$). |
| Voltmeters | Instruments used to measure potential difference, connected in parallel with the component across which the voltage is measured. They have high resistance. |
| Electromotive force (e.m.f.) | The maximum potential difference across the terminals of a source when no current is flowing; it represents the energy transferred per unit charge from chemical to electrical energy. |
| Resistance | The opposition to the flow of electric current in a conductor. |
| Ohm (Ω) | The SI unit of resistance. |
| Resistors | Components designed to have a specific resistance, used to control current and voltage in circuits. |
| Ohm's law | States that the current through a metallic conductor is directly proportional to the potential difference across it, provided the temperature remains constant ($V = IR$). |
| Ohmic conductors | Conductors that obey Ohm's law, where resistance is constant regardless of voltage or current. |
| Non-ohmic conductors | Conductors whose resistance changes with voltage, current, or temperature (e.g., diodes, filament lamps, thermistors). |
| Thermistors | Resistors whose resistance changes significantly with temperature, often decreasing as temperature increases. |
| Light-dependent resistors (LDRs) | Resistors whose resistance decreases as the intensity of light falling on them increases. |
| Potential divider | A series circuit of resistors used to provide a variable output voltage from a fixed supply voltage. |
| Resistivity (ρ) | A material property that quantifies its resistance to electrical current, independent of its shape ($R = \rho l/A$). |
| Capacitance | The ability of a capacitor to store electric charge, measured in farads (F). |
| Farad (F) | The SI unit of capacitance. |
| Capacitors | Electronic components that store electric charge, consisting of two conductors separated by an insulator (dielectric). |
| Charging and discharging | The processes by which a capacitor stores and releases electric charge, often through a resistor. |
| Diode | A semiconductor device that allows current to flow in one direction only. Used for rectification. |
| Rectification | The process of converting alternating current (a.c.) to direct current (d.c.) using diodes. |
| Transistors | Semiconductor devices with three terminals that can act as amplifiers or switches, revolutionizing electronics. |
| Transistor as a switch | Using a small input signal to control a larger output current, providing fast and reliable switching without moving parts. |
| Logic gates | Electronic switching circuits that perform logical operations on binary inputs (0s and 1s) to produce a specific output. |
| NOT gate | Inverts the input: output is 1 if input is 0, and 0 if input is 1. |
| OR gate | Output is 1 if either input A OR input B (or both) is 1. |
| NOR gate | Output is 1 only if neither input A NOR input B is 1. |
| AND gate | Output is 1 only if both input A AND input B are 1. |
| NAND gate | Output is 1 if input A AND input B are NOT both 1. |
| Truth table | A table that shows the output of a logic gate for all possible combinations of input values. |
| Analogue electronics | Circuits where voltages or currents vary continuously over a range. |
| Digital electronics | Circuits where voltages have only two distinct states (high/low or 1/0), used in computing and logic. |
| Transducers | Devices that convert energy from one form to another, often between non-electrical and electrical forms. |
| Input transducer (sensor) | Detects environmental changes and converts them into electrical signals (e.g., LDR, thermistor, microphone). |
| Output transducer | Converts electrical energy into another form (e.g., lamp, loudspeaker, motor). |
| Relays | Switches operated by an electromagnet, used to control higher power circuits with low power signals. |
| Light-emitting diodes (LEDs) | Semiconductor devices that emit light when forward-biased. |
| Generators | Devices that convert mechanical energy into electrical energy through electromagnetic induction. |
| Electromagnetic induction | The process of inducing a voltage (and potentially a current) in a conductor when it is exposed to a changing magnetic field or moves through a magnetic field. |
| Faraday's law | States that the magnitude of the induced e.m.f. is directly proportional to the rate at which the magnetic field lines are cut. |
| Lenz's law | States that the direction of an induced current is such that it opposes the change that produced it. |
| Fleming's right-hand rule | A mnemonic to determine the direction of the induced current in a conductor moving in a magnetic field. |
| Alternator (a.c. generator) | A generator that produces alternating current, typically using slip rings to connect the rotating coil to the external circuit. |
| Dynamo (d.c. generator) | A generator that produces direct current, typically using a commutator to reverse the connections to the coil as it rotates. |
| Practical generators | Generators used in power stations, cars, and bicycles, often employing electromagnets and multiple coils for higher efficiency and power output. |
| Transformers | Devices that change alternating voltages to higher or lower values using mutual induction between two coils wound on a soft iron core. |
| Mutual induction | The induction of a voltage in one coil due to a changing current in a nearby coil. |
| Transformer equation | Relates the voltages and the number of turns in the primary and secondary coils ($V_s/V_p = N_s/N_p$). |
| Eddy currents | Currents induced in a conductive core due to a changing magnetic field, which can cause heating and energy loss. Laminated cores reduce these losses. |
| Transmission of electrical power | The process of sending electrical energy over long distances, typically using high voltages and low currents to minimize energy loss as heat. |
| Electromagnets | Magnets created by electric current, used in various devices like motors, relays, and bells. |
| Electric motors | Devices that convert electrical energy into mechanical energy, utilizing the force experienced by a current-carrying conductor in a magnetic field. |
| Fleming's left-hand rule | A mnemonic to determine the direction of the force on a current-carrying conductor in a magnetic field. |
| Moving-coil loudspeakers | Devices that convert electrical signals into sound waves using a coil attached to a cone, vibrating within a magnetic field. |
| Electric meters | Instruments used to measure electrical quantities such as current, voltage, resistance, power, and energy. |
| Galvanometers | Sensitive instruments used to detect and measure small currents or potential differences, typically employing a moving coil in a magnetic field. |
| Ammeters | Galvanometers modified with a low-resistance shunt in parallel to measure current, connected in series. |
| Voltmeters | Galvanometers modified with a high-resistance multiplier in series to measure potential difference, connected in parallel. |
| Multimeters | Versatile instruments capable of measuring voltage, current, and resistance, often with both analogue and digital displays. |
| Cathode rays | Beams of high-speed electrons emitted from a hot cathode in a vacuum tube. |
| Thermionic emission | The emission of electrons from a heated surface. |
| Maltese cross tube | An evacuated glass tube used to demonstrate the straight-line motion and deflection of cathode rays by electric and magnetic fields. |
| Deflection of electron beams | Electron beams can be deflected by both electric fields (due to force on charge) and magnetic fields (due to force on moving charge), following parabolic or circular paths respectively. |
| Cathode Ray Oscilloscope (CRO) | An instrument that displays the variation of an electrical signal with time on a fluorescent screen, using an electron beam deflected by electric fields. |
| X-rays | High-energy electromagnetic radiation produced when high-speed electrons strike a metal target, used in medical imaging and industry. |
| Photoelectric effect | The emission of electrons from a material when light or other electromagnetic radiation of sufficient frequency shines on it. |
| Waves or particles | The dual nature of electromagnetic radiation, exhibiting both wave-like and particle-like properties depending on the phenomenon observed. |
| Radioactivity | The spontaneous emission of radiation from unstable atomic nuclei. |
| Ionising effect of radiation | The ability of radiation (alpha, beta, gamma) to remove electrons from atoms, creating ions. |
| Geiger-Müller (GM) tube | A device used to detect and count ionizing radiation by amplifying the electrical pulses produced when radiation passes through a gas. |
| Alpha (α) particles | Positively charged helium nuclei ($^4_2$He) emitted during radioactive decay; they are highly ionizing but have a short range. |
| Beta (β) particles | High-energy electrons ($\beta^-$) or positrons ($\beta^+$) emitted during radioactive decay; they are less ionizing than alpha particles but more penetrating. |
| Gamma (γ) rays | High-energy electromagnetic radiation emitted from atomic nuclei; they are highly penetrating, not deflected by fields, and ionize weakly. |
| Particle tracks | Visible paths left by ionizing radiation in cloud chambers or bubble chambers, showing their trajectory and interactions. |
| Radioactive decay | The process by which unstable atomic nuclei transform into more stable ones by emitting radiation. |
| Half-life | The average time it takes for half of the radioactive atoms in a sample to decay. |
| Activity | The rate at which radioactive decays occur in a sample, often measured in counts per second or minute. |
| Random nature of decay | Radioactive decay is a spontaneous, random process, meaning the exact time of decay for a specific atom cannot be predicted. |
| Uses of radioactivity | Thickness gauging, tracers in medicine and industry, radiotherapy, sterilization, and archaeological dating (carbon-14 dating). |
| Dangers and safety | Radiation can cause cell damage, mutations, cancer, and radiation sickness. Safety measures include distance, shielding, limiting exposure time, and using appropriate detectors. |
| Atomic structure | The composition of atoms, including protons, neutrons, and electrons. |
| Nucleus | The dense, positively charged core of an atom containing protons and neutrons. |
| Protons | Positively charged particles found in the nucleus of an atom; their number defines the element. |
| Neutrons | Uncharged particles found in the nucleus of an atom; they contribute to the mass. |
| Electrons | Negatively charged particles orbiting the nucleus; their arrangement determines chemical properties. |
| Nucleon number (A) | The total number of protons and neutrons in an atomic nucleus. |
| Proton number (Z) | The number of protons in the nucleus, defining the element (also called atomic number). |
| Isotopes | Atoms of the same element (same proton number) but with different numbers of neutrons (different nucleon number). |
| Nuclides | A distinct type of atom characterized by its specific number of protons and neutrons. |
| Radioactive decay equations | Nuclear reactions showing the transformation of unstable nuclei through the emission of alpha, beta, or gamma radiation. |
| Nuclear stability | The balance between protons and neutrons within a nucleus that determines whether it is stable or radioactive. |
| Models of the atom | Theories describing the structure of atoms, such as the 'plum pudding' model, Rutherford's nuclear model, and Bohr's planetary model, and the more modern quantum mechanical (electron cloud) model. |
| Nuclear energy | Energy released from atomic nuclei through processes like fission and fusion, related to the conversion of mass into energy ($E=mc^2$). |
| Fission | The splitting of a heavy atomic nucleus into lighter nuclei, releasing energy and neutrons, which can lead to a chain reaction. |
| Fusion | The combining of light atomic nuclei to form heavier ones, releasing energy (e.g., in stars and hydrogen bombs). |