Momentum & Impulse

Momentum describes how hard it is to stop a moving object, and it depends on both mass and velocity. In physics, momentum is important because it helps explain collisions, recoil, and why heavier or faster objects are harder to bring to rest. Since momentum has direction, it is treated as a vector quantity. This makes it useful for analyzing motion in one or more dimensions.

Impulse connects force and time to changes in momentum during a collision. A large force acting for a short time can produce the same impulse as a smaller force acting for a longer time, as long as the product of force and time is the same. This idea explains why airbags, helmets, and crumple zones reduce injury by increasing collision time. In isolated systems, total momentum is conserved, so momentum before a collision equals momentum after the collision.

Key Facts

Momentum is given by p = mv
Momentum is a vector, so direction matters when adding or subtracting momentum
Impulse is J = FΔt
Impulse equals change in momentum: J = Δp = mvf - mvi
If no external net force acts on a system, total momentum is conserved: Σpi = Σpf
Increasing collision time lowers average force for the same change in momentum: Favg = Δp/Δt

Vocabulary

Momentum: The quantity of motion of an object, equal to its mass multiplied by its velocity.
Impulse: The effect of a force acting over a time interval, equal to the change in momentum.
Vector quantity: A physical quantity that has both magnitude and direction.
Conservation of momentum: The rule that total momentum stays constant in a closed system with no external net force.
Collision time: The duration over which two objects interact during a collision.

Common Mistakes to Avoid

Ignoring direction when calculating momentum, which is wrong because momentum can be positive or negative depending on the chosen axis.
Using speed instead of velocity, which is wrong because momentum requires direction as part of the calculation.
Assuming a bigger force always means a bigger impulse, which is wrong because impulse depends on both force and time.
Applying conservation of momentum to a system with significant external forces, which is wrong because outside forces can change the total momentum of the system.

Practice Questions

1 A 4.0 kg cart moves to the right at 3.0 m/s. What is its momentum?
2 A 0.20 kg ball changes velocity from 8.0 m/s to the right to 2.0 m/s to the left in 0.050 s. Find the change in momentum and the average force on the ball.
3 Two identical eggs are dropped from the same height, but one lands on concrete and the other lands on a thick cushion. Explain why the cushion reduces the force on the egg using impulse and collision time.