Unit 4: Linear Momentum

What this unit is about

A football player tackles another. A car's airbag opens. A skater pushes off a wall. Two carts crash on a track. In every case, forces act for a short time and objects change how they move. Momentum is the tool that makes these problems easy: it lets you skip the messy details of the crash and compare "before" with "after".

By the end you will be able to find the momentum of an object and a system, use impulse to find average forces in collisions, use conservation of momentum to predict what happens after a crash or an explosion, and tell elastic from inelastic collisions with kinetic energy.

Exam weight

On the AP Physics 1 exam (course framework effective fall 2024), Unit 4 is 10–15% of the multiple-choice score. Momentum also shows up inside free-response questions, often mixed with energy (Unit 3) or with rotation (Unit 6, angular momentum).

Key equations from the AP equation sheet: p = mv, J = FavgΔt = Δp, Fnet = Δp/Δt, vcm = Σmv / Σm, and K = ½mv² for checking collisions.

Topics

  1. 4.1 Linear Momentum
    Momentum is mass times velocity, a vector; the momentum of a system is the vector sum, and it equals total mass times the centre of mass velocity.
  2. 4.2 Change in Momentum and Impulse
    A force acting over time gives an impulse that equals the change in momentum; impulse is the area under a force-time graph, so a longer stop means a smaller force.
  3. 4.3 Conservation of Linear Momentum
    If the net external force on a system is zero, its total momentum stays the same, in crashes, explosions and recoils.
  4. 4.4 Elastic and Inelastic Collisions
    Momentum is conserved in every collision of an isolated system; kinetic energy is conserved only in elastic ones, and objects that stick together lose the most.

Play and practise

How to study this unit

  1. Go through 4.1 to 4.4 in order. In each lab, use Predict first before pressing Play.
  2. Try each example yourself before opening the solution.
  3. Play the games until you pass the hardest level of each.
  4. Do the practice set in one sitting, then mark it with the scoring guides.