Momentum GCSE physics questions use the formula p = mv: momentum equals mass multiplied by velocity, measured in kilograms metres per second (kg m/s). It is a vector quantity, so direction matters. In a closed system, total momentum before a collision or explosion always equals total momentum after — the principle of conservation of momentum.
What is momentum?
Momentum is a measure of how much motion an object has, combining how heavy it is with how fast it is moving. Every momentum GCSE physics question starts from the same formula:
momentum (kg m/s) = mass (kg) × velocity (m/s)
or, using symbols:
p = m × v
Momentum is measured in kilogram metres per second (kg m/s). Because velocity is a vector (it has direction), momentum is also a vector quantity — a heavy lorry moving north has momentum in a different direction from an identical lorry moving south, even at the same speed.
How do you calculate momentum?
To calculate momentum, multiply an object's mass by its velocity. Direction is usually shown with a positive or negative sign, or stated in words.
Worked example 1: A 5 kg shopping trolley moves at 2 m/s. What is its momentum?
- p = m × v
- p = 5 × 2 = 10 kg m/s
Worked example 2: A 900 kg car travels at 20 m/s due east. What is its momentum?
- p = m × v
- p = 900 × 20 = 18,000 kg m/s due east
Worked example 3 (rearranging the formula): An object has a momentum of 60 kg m/s and a mass of 12 kg. What is its velocity?
- v = p ÷ m
- v = 60 ÷ 12 = 5 m/s
What is conservation of momentum?
The principle of conservation of momentum states that in a closed system, with no external forces acting, the total momentum before an event equals the total momentum after the event. This applies to collisions, explosions, and objects pushing apart from each other.
total momentum before = total momentum after
This is one of the most heavily tested ideas in GCSE physics because it lets you calculate an unknown velocity or mass after a collision, provided everything else is known.
Worked example: conservation of momentum in a collision
A 2 kg trolley moving at 3 m/s collides with a stationary 1 kg trolley, and the two trolleys stick together (an inelastic collision). What is their combined velocity immediately after the collision?
Step 1 — find total momentum before the collision:
| Trolley | Mass (kg) | Velocity (m/s) | Momentum (kg m/s) |
|---|---|---|---|
| A | 2 | 3 | 2 × 3 = 6 |
| B | 1 | 0 | 1 × 0 = 0 |
| Total | 6 |
Step 2 — apply conservation of momentum:
Total momentum after = total momentum before = 6 kg m/s
Step 3 — find the combined velocity:
Combined mass = 2 + 1 = 3 kg
- v = p ÷ m
- v = 6 ÷ 3 = 2 m/s
The two trolleys move off together at 2 m/s, in the direction Trolley A was originally travelling.
How does conservation of momentum apply to explosions?
Conservation of momentum also applies when objects push apart, such as a firework exploding or a person jumping off a stationary skateboard. Before the explosion, if everything is at rest, the total momentum is zero. After the explosion, the momentum of the pieces moving in one direction must exactly balance the momentum of the pieces moving in the opposite direction, so the total still equals zero.
Worked example: A 60 kg skater standing at rest on a 4 kg skateboard pushes off. The skateboard shoots backward at 3 m/s. What is the skater's velocity?
- Total momentum before = 0 (everything at rest)
- Momentum of skateboard after = 4 × 3 = 12 kg m/s (backward)
- Momentum of skater after must be 12 kg m/s forward, so the total remains 0
- v = p ÷ m = 12 ÷ 60 = 0.2 m/s forward
Frequently asked questions
What is the formula for momentum?
Momentum equals mass multiplied by velocity, written as p = m × v. Mass is measured in kilograms and velocity in metres per second, giving momentum the unit kilogram metres per second (kg m/s). Because velocity includes direction, momentum is a vector quantity, so the direction of motion must always be stated alongside the numerical answer.
What is conservation of momentum?
Conservation of momentum states that in a closed system with no external forces, the total momentum before an event — such as a collision or explosion — equals the total momentum after it. This principle allows you to calculate an unknown mass or velocity after a collision, as long as the other quantities are known.
Is momentum a vector or a scalar quantity?
Momentum is a vector quantity because it depends on velocity, which has both magnitude and direction. Two objects with the same mass and speed but travelling in opposite directions have momentum of equal size but opposite direction, and their momenta can cancel out when added together, which is central to solving collision problems.
What is the difference between mass and momentum?
Mass is the amount of matter in an object, measured in kilograms, and stays the same regardless of motion. Momentum depends on both mass and velocity, so a stationary object always has zero momentum even though it still has mass. A small, fast-moving object can have the same momentum as a large, slow-moving one.
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