Mechanics
The Mechanics domain tests motion, forces, energy, momentum, circular motion, and gravitation. Expect free-body diagrams, kinematics graphs, conservation laws, and multi-step problems combining forces and energy.
Core rules
Use Newton’s second law, ΣF = ma, with a consistent sign convention. On an incline, the normal force is perpendicular to the surface and equals mg cosθ only when no other perpendicular forces act. Friction opposes relative motion and has magnitude μN. Work is Fd cosθ; the work-energy theorem says net work equals ΔK. Mechanical energy is conserved when only conservative forces do work. Momentum is conserved in collisions when external impulse is negligible.
Worked example
A 2.0 kg block starts from rest and slides 5.0 m down a 30° incline with μk = 0.20. Find its speed at the bottom. The gravity component along the incline is mg sinθ = 2.0(9.8)(0.50) = 9.8 N, doing 49 J. Normal force is mg cosθ = 2.0(9.8)(0.866) = 17.0 N, so friction is 0.20(17.0) = 3.4 N, doing −17 J over 5.0 m. Net work is 32 J. Set 32 = ½(2.0)v², so v² = 32 and v ≈ 5.7 m/s. The reasoning matters: use the incline component of weight, not mg, and subtract friction work.
Traps
Mass is not weight. Normal force is not always mg. Centripetal force is a net force requirement, not an extra force to add. Action–reaction pairs act on different objects. In projectile motion, horizontal velocity is constant when drag is ignored.