Momentum, Impulse, and Collisions

A moving truck and a moving tennis ball can have the same speed, but stopping them is a very different job. Momentum accounts for both mass and velocity.

This lesson supports Chapter 6 of High School Physics.

Momentum is a vector

Linear momentum is \[\vec p=m\vec v.\] Its direction matches the velocity. A large mass, a large speed, or both produce a large momentum. In one-dimensional problems, choose a positive direction and give motion in the opposite direction a negative velocity.

Impulse changes momentum

Impulse is the product of average net force and contact time: \[\vec J=\vec F_{\text{net,avg}}\Delta t=\Delta\vec p.\] Airbags and padded mats increase stopping time. For the same nonzero momentum change, a longer stopping time means a smaller average net-force magnitude. They do not remove the momentum change.

Momentum is conserved in an isolated system

If the external impulse is negligible, total momentum before a collision equals total momentum after it. Kinetic energy is also conserved in an elastic collision. In an inelastic collision, some kinetic energy becomes thermal energy, sound, or deformation. Objects that stick together undergo a perfectly inelastic collision.

Worked example

A \(2\text{ kg}\) cart moving right at \(3\text{ m/s}\) sticks to a \(1\text{ kg}\) cart at rest. Assuming negligible external horizontal impulse during the collision, conservation of momentum gives \(2(3)+1(0)=(2+1)v_f\), so \(v_f=2\text{ m/s}\) to the right.

Watch the idea in action

Professor Dave Explains gives a focused explanation of the chapter’s central idea. Pause before each calculation and predict the next step on paper.

Practice questions

1. Write the momentum formula.
2. Is momentum a scalar or a vector?
3. How is impulse related to momentum?
4. Why does an airbag reduce average force?
5. What is conserved in every isolated collision?
6. What makes a collision perfectly inelastic?

Answers

1. \(\vec p=m\vec v\).
2. A vector.
3. Impulse equals the change in momentum.
4. It increases stopping time for the same momentum change, reducing the average net-force magnitude.
5. Total momentum.
6. The objects stick together.

Keep studying

High School Physics includes 12 full-length practice tests: two in the book and ten online.

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