IGCSE Physics Motion notes

Physics starts with measurement. A rule measures length; you read it with your eye directly above the mark to avoid a parallax error, and you quote the reading to the smallest division of the scale. A measuring cylinder measures the volume of a liquid: you read the volume at the bottom of the meniscus (the curved surface of the liquid), again with the eye level with the mark.

To find the volume of an irregular solid, such as a stone or a model dinosaur, lower it into a measuring cylinder partly filled with water. The rise in the water level equals the volume of the object. This is called finding volume by displacement, and it only works for objects that sink.

Time intervals are measured with clocks and stopwatches; a digital timer that is started and stopped automatically (for example by a light gate) is more accurate than a human pressing a button, because human reaction time is around 0.2 s.

Supplement: quantities are either scalars, which have size (magnitude) only, or vectors, which have size and direction. Distance, speed, time, mass, energy and temperature are scalars. Force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength are vectors. Saying "a velocity of 5 m/s" is incomplete — "a velocity of 5 m/s upwards" is not.

1. 1Draw the arrows

   Draw the two vectors head-to-tail at right angles, e.g. a 3 N force east and a 4 N force north.

2. 2Close the triangle

   The resultant runs from the start of the first arrow to the end of the second.

3. 3Calculate

   Pythagoras: resultant = √(3² + 4²) = √25 = 5 N. The direction is at tan θ = 4/3 ≈ 53° north of east.

Speed is the distance travelled per unit time: v = s/t. Its SI unit is the metre per second (m/s). Velocity is speed in a given direction — a vector. If a car drives once around a roundabout at a steady 30 km/h, its average speed is 30 km/h but its average velocity is zero, because it ends where it started.

Supplement: acceleration is the change in velocity per unit time: a = Δv/Δt, measured in metres per second squared (m/s²). If a cyclist speeds up from 4.0 m/s to 10.0 m/s in 3.0 s, then a = (10.0 − 4.0) ÷ 3.0 = 2.0 m/s². A deceleration is just a negative acceleration: the velocity is decreasing, so Δv is negative.

For an object near the Earth’s surface with air resistance ignored, falling objects accelerate downwards at approximately g = 9.8 m/s² — the acceleration of free fall. It is approximately constant close to the ground.

On a distance–time graph, a straight sloping line means constant speed; a steeper line means a faster speed; a curve that gets steeper means the object is speeding up (accelerating). The speed on any straight section is the gradient: divide the change in distance by the change in time, using values read from the axes.

On a speed–time graph, a horizontal line means constant speed, a straight sloping line means constant acceleration, and a curve means changing acceleration. The area under the graph gives the distance travelled — for constant speed the area is a rectangle (v × t); for constant acceleration it is a triangle (½ × base × height) or a trapezium.

Supplement: falling objects show both ideas at once. At the moment of release only weight acts, so the object accelerates downwards at g ≈ 9.8 m/s². As speed grows, air resistance grows too, so the resultant force — and hence the acceleration — shrinks: the speed–time graph curves, levelling off. When air resistance has grown enough to equal the weight, the resultant force is zero and the object falls at a constant terminal velocity. A skydiver who opens a parachute suddenly has much larger drag: the terminal velocity drops from tens of m/s to a few m/s.

Mass is a measure of the quantity of matter in an object, measured in kilograms (kg). Mass does not change from place to place. Weight is a gravitational force on an object that has mass, measured in newtons (N) — it is a vector, and it does change from place to place: you weigh less on the Moon, but your mass is unchanged.

Gravitational field strength g is defined as force per unit mass: g = W/m. Its unit is N/kg — and this is numerically the same as the acceleration of free fall in m/s², because a free-falling object of any mass gains 9.8 m/s of speed every second. Near the Earth’s surface, g ≈ 9.8 N/kg.

Weights — and masses — can be compared using a balance: a balance compares the weights of two objects, so when the beam balances, their masses are equal too. Supplement: the cleanest way to say all this: weight is the effect of a gravitational field on a mass. Where the field is stronger, the same mass feels a larger force.

Density is defined as mass per unit volume: ρ = m/V. Its common units are kg/m³ and g/cm³ (1 g/cm³ = 1000 kg/m³, because 1 kg = 1000 g and 1 m³ = 10⁶ cm³). A block of the same size as another but with twice the mass has twice the density.

• Liquid: weigh an empty measuring cylinder, add the liquid, weigh again; the mass of liquid is the difference. Read the volume from the cylinder and divide.
• Regular solid (e.g. a block): measure its length, width and height with a rule, calculate the volume, then divide mass by volume.
• Irregular solid that sinks: find its mass, then lower it into a measuring cylinder of water and read the rise in level — the displaced volume equals the object’s volume.

Floating: an object floats in a liquid if its density is lower than the liquid’s — ice (≈0.92 g/cm³) floats on water (1.0 g/cm³). Supplement: the same rule decides which of two immiscible liquids floats on which: oil (≈0.8 g/cm³) floats on water because it is less dense, and any liquid denser than water would sink below it.