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
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.
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.
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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