Classical Mechanics
Classical Mechanics is the largest block of the GRE Physics Subject Test, at roughly 20% of the questions. It covers Newtonian particle and rigid-body dynamics, work and energy, momentum and collisions, gravitation and orbital motion, and small oscillations. Most items are one- or two-step calculations, but they reward a clean setup: choosing coordinates, spotting the conserved quantity, and knowing when rotational or Lagrangian reasoning shortcuts the algebra.
Core rules
- Newton's second law in component form. On an incline, gravity contributes mg sinθ along the plane and mg cosθ normal to it.
- Energy methods apply when forces are conservative; kinetic friction removes f_k d = μ_k N d from the mechanical energy.
- Linear momentum is conserved when no external impulse acts; kinetic energy is conserved only in elastic collisions. In the center-of-mass frame an elastic collision simply reverses each velocity.
- The center of mass moves as if all external forces acted there; for two-body problems the reduced mass μ = m₁m₂/(m₁+m₂) turns relative motion into a one-body problem.
- Rigid bodies: τ = Iα about a fixed axis, with I computed about that same axis (parallel-axis theorem I = I_cm + Md²).
- Orbits: circular speed v = √(GM/r), period T² ∝ a³, total energy E = −GMm/2a.
- Small oscillations: ω = √(k/m) for a spring, √(g/L) for a pendulum at small amplitude.
Worked example
A 2 kg block slides 3 m down a 30° incline with μ_k = 0.25. Find its speed from rest. The normal force is N = mg cos30° = 2(9.8)(0.866) = 17.0 N, so friction is f = 0.25(17.0) = 4.24 N. Along the plane, mg sin30° = 9.8 N. Net force = 9.8 − 4.24 = 5.56 N, so a = 2.78 m/s². Then v² = 2as = 2(2.78)(3) = 16.7, giving v ≈ 4.1 m/s. The energy check agrees: mgh − fd = 2(9.8)(1.5) − 4.24(3) = 29.4 − 12.7 J.
Traps
Sign errors in g and in the friction direction; using I about the center of mass when the body pivots elsewhere; forgetting that tension does work in a pulley system; assuming momentum is conserved when gravity or a pivot exerts an external impulse during the interval; applying the small-angle approximation beyond roughly 10–15°.