Mechanics: Kinematics, Dynamics, Statics, Conservation Laws
Core concepts
Kinematics describes motion without asking why: distinguish displacement from distance, velocity from speed, and average from instantaneous values. For constant acceleration use the standard relations (v = v₀ + at, s = v₀t + at²/2, v² = v₀² + 2as). For projectile motion, treat horizontal and vertical components independently, with a = g downward only.
Dynamics rests on Newton's three laws. Always draw a free-body diagram before writing ΣF = ma; resolve forces along convenient axes. Friction obeys f ≤ μN, with equality at the threshold of slipping. For circular motion, the net inward force equals mv²/r.
Statics requires ΣF = 0 and Στ = 0. Choose the pivot to eliminate unknown forces. For a rigid body, torque is τ = F·d·sinθ about the chosen axis.
Conservation laws often bypass force analysis. Momentum is conserved in collisions and explosions (vectorially); kinetic energy is conserved only in elastic collisions. Mechanical energy is conserved when only conservative forces do work; otherwise use the work–energy theorem W_net = ΔK.
Traps
- Mixing up displacement and path length in average-speed questions.
- Forgetting that g acts throughout projectile flight, including at the top.
- Sign errors when decomposing forces on inclines.
- Assuming kinetic energy conservation in inelastic collisions.
- Using the wrong lever arm in torque problems.
Worked rule of thumb
For an elastic collision of equal masses with one initially at rest, the moving body stops and the struck body takes its velocity - a quick check that your algebra is consistent.