Mechanics
Mechanics covers kinematics, Newton's laws, momentum, energy, circular motion, and gravitation - the largest quantitative share of the exam. Items reward clean free-body diagrams and conservation reasoning over formula hunting.
Core rules
- Kinematics. For constant acceleration use v = v₀ + at, Δx = v₀t + ½at², and v² = v₀² + 2aΔx. Pick a positive direction and keep it throughout.
- Newton's second law. ΣF = ma applies along each axis independently. Weight is mg (a force); mass is in kilograms.
- Friction. f_s ≤ μ_sN and f_k = μ_kN. Normal force is not automatically mg - on an incline, N = mg cos θ.
- Momentum and energy. With no external net force, Σp is conserved. Mechanical energy is conserved only when non-conservative work is zero.
- Circular motion. The centripetal force is the net inward force, not an extra force; a_c = v²/r.
Worked example
A 2.0 kg block is pushed horizontally with 12 N across a level floor where μ_k = 0.25. Find the acceleration. Normal force N = mg = 2.0 × 9.8 = 19.6 N, so friction f_k = 0.25 × 19.6 = 4.9 N. Net force = 12 − 4.9 = 7.1 N. Then a = 7.1/2.0 = 3.55 ≈ 3.6 m/s².
Traps
- Writing F = ma with F as an applied force instead of the net force.
- Switching between g = 9.8 and g = 10 mid-problem.
- Forgetting that constant velocity means zero net force, not zero applied force.
- Assuming kinetic energy is conserved in every collision - momentum is, kinetic energy is not.