Impulse–momentum theorem

Beginner

Impulse equals the change in momentum.

Key relationFΔt = mΔv

FΔt = mΔv ties force and time to velocity change. It's the main tool for impacts when the force is unknown but time is known.

Worked example

A 0.2 kg ball changes from 10 to −10 m/s in 0.01 s: F_avg = 400 N.

Common mistake

Average force, not peak force.

In more detail

The impulse-momentum theorem states that the impulse on an object equals its change in momentum, FΔt = Δp. It works for variable forces with the average force used.

Real-world uses

Estimating the force on a car that hits a barrier, using its change in momentum over the crash time.
Designing padded surfaces to extend the stopping time of falling athletes.
Engineers calculate the change in momentum of a falling object hitting a crash barrier to size the barrier's force correctly.

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Frequently asked questions

Is it the same as Newton's second law?

Yes, the impulse form is the integrated version of F = dp/dt.

What if the force is not constant?

Use the average force over the interval, or integrate the force with respect to time.

Is the impulse equal to the force times the time for a changing force?

Only for a constant force. For a changing force, the impulse is the integral of force with respect to time.

Impulse–momentum theorem

In more detail

Real-world uses

Frequently asked questions

Related topics in Momentum & Collisions