These units introduce conservation laws — energy and momentum — which are among the most powerful tools in physics. Many AP problems are best solved using these principles rather than force analysis.
Work W = Fd cosθ (joules). Work-energy theorem: W_net = ΔKE. KE = ½mv². Gravitational PE = mgh. Spring PE = ½kx². Conservation of energy: KE₁ + PE₁ + W_nc = KE₂ + PE₂ (W_nc = work by non-conservative forces like friction). Power P = W/t = Fv.
Momentum p = mv (vector). Impulse J = FΔt = Δp. Conservation of momentum: in isolated system (no external forces), total momentum is constant. Elastic collision: both momentum and KE conserved. Inelastic: momentum conserved, KE not. Perfectly inelastic: objects stick together. Explosions: reverse of collision (momentum conserved, KE increases from internal energy). 2D collisions: conserve momentum in x and y independently.
Use conservation of energy when: no external work done (or you know the work), you need to relate speeds at different positions, and you have height changes or springs. Use conservation of momentum when: objects interact (collisions, explosions), no significant external forces during the interaction, and you need final velocities after collision. Often you need BOTH: momentum conserved during collision to find velocities, then energy to analyse motion before/after. Key: energy is a scalar (easier algebra); momentum is a vector (must consider direction).
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