AshPhys

The idea of momentum

AshPhys · Revision cheat sheet
AS Level9702 AS Ch.6Chapter 6: MomentumLesson 6.1Sections 6.1

Goal: Calculate momentum and the change in momentum, with the direction as a sign.

velocity

01The big picture

Momentum is mass × velocity. It is a vector: choose a positive direction, and an object moving the other way has negative momentum. Its unit is kg m s⁻¹ (the same as N s).

When an object rebounds, its velocity changes sign, so the change in momentum is larger than either momentum on its own: Δp=mv−mu\Delta p = mv - mu with vv negative.

Linear momentum [paraphrase]
The product of an object’s mass and its velocity.
Fig. 1 · A ball rebounds from a wall
A ball rebounds from a wallBefore: a ball moves to the right towards a wall at 25 m/s. After: the ball moves to the left away from the wall at 15 m/s, shown by a shorter arrow.beforeafter+25 m s⁻¹−15 m s⁻¹+ direction
The velocity changes sign, so Δp=m(v−u)\Delta p = m(v - u) is bigger than mumu or mvmv.

02Key equations

Momentum
p=mvp = mv
Change in momentum
Δp=mv−mu\Delta p = mv - mu
Symbols and units
  • ppmomentumkg m s−1\mathrm{kg\,m\,s^{-1}}
  • mmmasskg\mathrm{kg}
  • u, vu,\ vvelocity before, afterm s−1\mathrm{m\,s^{-1}}

03Sample problems with solutions

Sample 1 · A rebound
A 0.060 kg ball hits a wall at 25 m s⁻¹ and rebounds along the same line at 15 m s⁻¹ (Fig. 1). Calculate the change in its momentum.

  1. Towards the wall is positive, so u=+25u = +25 and v=−15v = -15 m s⁻¹:

    Δp=m(v−u)=0.060 (−15−25)\Delta p = m(v - u) = 0.060\,(-15 - 25)

  2. Evaluate:

    Δp=−2.4 kg m s−1\Delta p = -2.4\ \mathrm{kg\,m\,s^{-1}}
Answer: 2.4 kg m s⁻¹, directed away from the wall
Unit check: kg×m s−1=kg m s−1 ✓\mathrm{kg} \times \mathrm{m\,s^{-1}} = \mathrm{kg\,m\,s^{-1}}\ \checkmark

04Practice problems

  1. P1
    Find the momentum of a 70 kg runner moving at 8.0 m s⁻¹.
    Final answer560 kg m s⁻¹
    Answer: 560 kg m s⁻¹
  2. P2
    A 0.40 kg ball has momentum 6.0 kg m s⁻¹. Find its speed.
    Final answer15 m s⁻¹
    Answer: 15 m s⁻¹
  3. P3
    A 2.0 kg trolley moves at +3.0 m s⁻¹ and a 1.5 kg trolley at −4.0 m s⁻¹. Find their total momentum.
    Final answerZero
    Answer: Zero
  4. P4
    A 0.20 kg ball hits the floor at 5.0 m s⁻¹ and bounces up at 3.0 m s⁻¹. Find the size of its change in momentum.
    Final answer1.6 kg m s⁻¹
    Answer: 1.6 kg m s⁻¹

05Other useful information

Common mistakes

  • ✗ Wrong: Rebound: Δp=m(25−15)\Delta p = m(25 - 15)

    ✓ Right: The velocity reverses: Δp=m(−15−25)\Delta p = m(-15 - 25)

  • ✗ Wrong: Add momenta as positive numbers.

    ✓ Right: Give each a sign for its direction first.

Exam tips

  • Draw an arrow for your positive direction before you write any velocity.

What the syllabus asks

  • 9702 topic 3: define and use linear momentum. Coursebook 6.1.

Explore: Practice questions for this lesson