Conservation of momentum: This is called conservation of momentum.

The idea

In a closed system, the total momentum before an event equals the total momentum after it, provided no external resultant force acts. This concept is assessed at Higher Tier only. Momentum p = m × v, measured in kg m/s, is a vector: assign one direction positive and the opposite negative. For two trolleys colliding and sticking, m₁u₁ + m₂u₂ = (m₁ + m₂)v. For a 2 kg trolley at 3 m/s hitting a stationary 1 kg trolley and sticking: total momentum before = 2 × 3 + 1 × 0 = 6 kg m/s; after, 3 kg × v = 6 kg m/s, so v = 2 m/s. The principle explains recoil, explosions and collisions, and follows from Newton's third law: equal and opposite forces act for equal times, so total momentum change is zero.

What earns the marks

• State that total momentum in a closed system is constant before and after an event.
• Define a closed system as one on which no external resultant force acts.
• Calculate momentum using p = m × v with mass in kg and velocity in m/s.
• Treat momentum as a vector, assigning opposite directions opposite signs.
• Apply m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ to collisions or explosions.
• Explain recoil or explosion using equal and opposite momentum changes.

Common mistakes and how to put them right

• Adding speeds instead of using signed velocities.

  Put it right: Assign one direction positive and the other negative before summing momenta.

• Forgetting to combine masses after a collision in which objects stick.

  Put it right: Use (m₁ + m₂) for the combined velocity.

• Using grams or km/h directly.

  Put it right: Convert to kg and m/s before calculating momentum.

Exam tips

• Write the momentum equation, substitute values with units, then solve for the unknown.
• State the direction of the final velocity, not just its magnitude.
• Check that total momentum before equals total momentum after as a final verification.
• As this is a Higher Tier only topic, be prepared to apply it alongside other concepts like kinetic energy.