Momentum, impulse and circular motion

Learning objectives

Define linear momentum as p = mv and impulse as J = FΔt, and obtain the impulse delivered by a varying force from the area under a force–time graph

Apply conservation of linear momentum to collisions and explosions in one and two dimensions, and classify a collision as elastic, inelastic or perfectly inelastic by comparing the total kinetic energy before and after

Express Newton's second law as F = Δp/Δt and apply it to situations such as a jet of water striking a surface or an average force acting over a measured contact time

Describe uniform circular motion using period, frequency, angular velocity ω = 2π/T and linear speed v = ωr, and explain why the velocity changes continuously although the speed is constant

Apply centripetal acceleration a = v²/r = ω²r and centripetal force F = mv²/r = mω²r to horizontal circles, vertical circles, banked tracks and conical pendulums, identifying in each case which real force supplies the centripetal force

Explain that the centripetal force in uniform circular motion does no work because it acts perpendicular to the velocity at every instant