Momentum

O Level / IGCSE Physics · Motion, forces and energy. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

Test this topic free All O Level / IGCSE Physics topics

The idea

Momentum is mass multiplied by velocity. A heavy lorry moving slowly and a light ball moving fast can have the same momentum. Momentum is a vector, so direction matters: choose one direction as positive and give the opposite direction a minus sign.

A resultant force changes the momentum of an object. The force multiplied by the time it acts is called the impulse, and it equals the change in momentum. For the same change in momentum, a longer time means a smaller force. This is why seat belts, air bags and crumple zones reduce injuries.

In a collision or an explosion with no outside forces, the total momentum before equals the total momentum after.

Rules to remember

momentum = mass × velocity (p = mv), in kg m/s
impulse = force × time (FΔt) = change in momentum Δ(mv), in N s
resultant force = change in momentum ÷ time taken (F = Δp/Δt)
Conservation of momentum: total momentum before = total momentum after, if no external force acts
If two objects stick together: m₁u₁ + m₂u₂ = (m₁ + m₂)v
Objects that start at rest and push apart have total momentum zero, so they move in opposite directions with equal sizes of momentum

Common mistake

Forgetting the direction when an object bounces back. A ball that arrives at 5 m/s and rebounds at 5 m/s has changed velocity by 10 m/s, not 0, so its momentum has changed.

Worked example

A trolley of mass 0.50 kg moves at 6.0 m/s and hits a stationary trolley of mass 1.5 kg. They stick together. What is their speed just after the collision?

Momentum before = (0.50 × 6.0) + (1.5 × 0) = 3.0 kg m/s
Mass after = 0.50 + 1.5 = 2.0 kg, so momentum after = 2.0 × v
Momentum is conserved: 2.0 × v = 3.0, so v = 3.0 ÷ 2.0 = 1.5 m/s

Answer: 1.5 m/s, in the direction the first trolley was moving.

Practice questions

Try each one, then open the answer.

1. A ball of mass 250 g rolls at 4.0 m/s. What is its momentum?

A
1.0 kg m/s
B
2.0 kg m/s
C
62.5 kg m/s
D
1000 kg m/s

Show answer

Answer: A. 250 g = 0.25 kg. Momentum = mv = 0.25 × 4.0 = 1.0 kg m/s. 2.0 is its kinetic energy in joules (½mv²); 1000 comes from leaving the mass in grams.

2. A ball of mass 0.40 kg moves at 5.0 m/s. What is its momentum?

A
0.08 kg m/s
B
2.0 kg m/s
C
5.4 kg m/s
D
12.5 kg m/s

Show answer

Answer: B. momentum = mass × velocity = 0.40 × 5.0 = 2.0 kg m/s.

3. Why do modern cars have crumple zones at the front?

A
to make the car lighter
B
to increase the time of the collision and so reduce the force
C
to increase the momentum of the car
D
to stop the car faster

Show answer

Answer: B. Force = change in momentum ÷ time. The momentum change is fixed, so a longer collision time gives a smaller force on the passengers.

Read the full notes

Keep going

← Forces Energy, work and power →All rules on one page Stuck? Ask a question