UnofficialAP Physics 1Unit 4 of 8

AP Physics 1 Unit 4: Linear Momentum

Impulse, collisions and conservation of momentum.

Unit overview

Momentum, $\vec{p} = m\vec{v}$ , is conserved for a system when the net external impulse is zero. That makes it the right tool for collisions and explosions, where internal forces are large, brief and hard to measure.

Impulse $\vec{J} = \vec{F}_{avg}\Delta t = \Delta\vec{p}$ explains why airbags and padding reduce force: they stretch the collision time for the same change in momentum. In an elastic collision kinetic energy is also conserved; in an inelastic one some becomes internal energy, and in a perfectly inelastic collision the objects stick together. The centre of mass of an isolated system moves with constant velocity.

Key topics

Impulse: Area under a force-time graph equals the change in momentum.
Conservation of momentum: Total momentum before equals total after for an isolated system.
Elastic and inelastic collisions: Momentum is always conserved; kinetic energy only in elastic collisions.
Centre of mass: Its velocity is unchanged by internal forces.

Worked example

A 3 kg cart moving at 4 m/s collides with and sticks to a stationary 1 kg cart. Find their common speed.

Momentum before: $3 \cdot 4 + 1 \cdot 0 = 12$ kg·m/s.
After: $(3 + 1)v = 12$ .
$v = 3$ m/s.

Answer: $v = 3$ m/s

Common mistakes

Ignoring direction: momentum is a vector, so velocities in opposite directions need opposite signs.
Assuming kinetic energy is conserved in every collision.
Applying conservation when a significant external force acts over the time interval.

Exam tips

State the system and why it is isolated before writing the conservation equation.
Check an inelastic answer by confirming the final kinetic energy is less than the initial.

See the AP Physics 1 exam format and every unit on the course page.