Mechanics
Domain 2: Mechanics
Mechanics covers kinematics graphs, Newton's three laws, friction, circular motion, work-energy, impulse-momentum, and rotation (torque, moment of inertia, angular momentum). The exam favors multi-step problems where choosing a conservation law or drawing a free-body diagram is the key decision.
Core rules
- Kinematics: v = v0 + at, Δx = v0t + ½at², v² = v0² + 2aΔx; these hold only for constant acceleration.
- Newton's second law is ΣF = ma per axis. Friction: fs ≤ μsN, fk = μkN, directed opposite impending or sliding motion.
- Work-energy: Wnet = ΔK; conservative forces have potential energy; mechanical energy is conserved only without nonconservative work.
- Impulse J = FΔt = Δp; momentum is conserved when the net external force is zero.
- Rotation: τ = rF sinθ = Iα; Krot = ½Iω²; L = Iω is conserved when the net external torque is zero.
Worked example
A 2.0 kg block slides down a 30° incline with μk = 0.25. Forces along the incline are mg sin30° downward and friction μkN upward, with N = mg cos30°. So a = g(sin30° − μk cos30°) = 9.8(0.500 − 0.217) = 2.8 m/s². Mass cancels; the normal force is mg cosθ, not mg.
Traps
- Setting N = mg on an incline or in an accelerating elevator.
- Adding a separate 'centripetal force' to a free-body diagram; tension, gravity, or friction supplies it.
- Applying momentum conservation when an external force such as gravity or a wall acts during the interval.
- Mixing angular and linear quantities, or using degrees in ω = 2πf.
- Assuming static friction always equals μsN; it takes whatever value is needed up to that maximum.