Physics

Momentum and Impulse

Momentum p = mv is the 'oomph' of motion. Impulse J = F·Δt is the change in momentum. In any collision or interaction, total momentum is conserved when no external force acts — the single most useful principle in collision problems.

How to Approach Momentum and Impulse

1

Set up before and after

List each object's mass and velocity before the collision, and the unknown velocities after. Conservation says: Σp_before = Σp_after.

2

Choose the collision type

Elastic: KE is also conserved (use a second equation). Perfectly inelastic: objects stick together, so v_final is shared. Anything in between: only momentum is conserved, not KE.

3

Solve the system

For elastic collisions: two equations (momentum + KE), two unknowns. For inelastic: one equation, easy algebra. Always check the signs of velocity — direction matters.

Frequently Asked Questions

What's the difference between momentum and KE?+

Both depend on mass and velocity, but momentum is linear in v (mv) while KE is quadratic (½mv²). KE is energy; momentum is a vector quantity tracking direction.

What is impulse useful for?+

When the force isn't constant or you only know the time interval. Impulse equals force times time, and equals change in momentum: F·Δt = m·Δv. Lets you solve collision problems without knowing F.

Is momentum always conserved?+

Only when no external force acts on the system. Internal forces (the objects pushing on each other) always cancel out via Newton's third law. External forces — friction, gravity over time — can change total momentum.

Related Topics

More step-by-step guides in Physics and adjacent subjects.

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