Inside This Unit: The Full Breakdown
This unit defines momentum and impulse (the integral of force over time), applies conservation of momentum to collisions and explosions, and uses the center of mass to analyze systems.
Why it matters
Momentum methods handle collisions and variable forces. Impulse as ∫F dt and the center-of-mass framework are emphasized in Physics C.
Key concepts
- Impulse J = ∫F dt = Δp (area under an F-t graph).
- Total momentum is conserved with no external force.
- Elastic collisions conserve KE; inelastic ones do not.
- The center of mass moves at constant velocity absent external forces.
Impulse and Momentum
Impulse is the integral of force over time and equals the change in momentum. For a time-varying collision force, the area under the F-t graph gives the impulse. The impulse-momentum theorem connects a force acting over time to a velocity change.
Conservation and Center of Mass
With no external force, system momentum is conserved — the basis for analyzing collisions, explosions, and recoil. Perfectly inelastic collisions have objects move together. The center of mass, the mass-weighted average position, moves at constant velocity when only internal forces act.
AP exam tip
In collisions, always conserve momentum first; only invoke kinetic-energy conservation if the collision is stated or shown to be elastic.
Connections to other units
- Unit 2: Impulse comes from forces acting over time.
- Unit 6: Angular momentum is the rotational analog of linear momentum.
