Classical Mechanics
Core concepts
Expect Newtonian dynamics in one and two dimensions, work–energy and impulse–momentum theorems, conservation laws, rotational motion (torque, moment of inertia, angular momentum), gravitation and orbits, simple harmonic motion, and an introduction to Lagrangian mechanics. Know when each conservation law applies and what symmetry underlies it: time translation gives energy conservation, spatial translation gives momentum, rotational invariance gives angular momentum.
Traps
- Non-conservative forces: friction changes mechanical energy; use work–energy with the friction term, not plain conservation.
- Moment of inertia depends on the axis; use the parallel-axis theorem I = I_cm + Md².
- Rolling without slipping couples v = ωR; a rolling object has both translational and rotational kinetic energy.
- Collisions: momentum is conserved in all collisions; kinetic energy only in elastic ones.
- SHM: ω = √(k/m) for a spring, √(g/L) for a pendulum; period is independent of amplitude only in the small-angle limit.
Worked example
A solid disk (I = ½MR²) rolls without slipping down a ramp of height h. Energy: Mgh = ½Mv² + ½Iω² = ½Mv² + ¼Mv² = ¾Mv², so v = √(4gh/3). A frictionless sliding block would reach √(2gh) - the disk is slower because energy goes into rotation.
Rule of thumb
Count constraints and conserved quantities first; often you can solve without integrating forces.