Mechanics: Kinematics, Dynamics, Statics, Gravitation, Rigid Bodies, Fluids
Core concepts
Mechanics questions reward a disciplined choice of reference frame and of the physical model. For kinematics you must move fluently between position, velocity and acceleration graphs, handle projectile motion with independent horizontal and vertical components, and treat uniform circular motion (a = v²/r directed to the centre). In dynamics, always draw a free-body diagram: Newton's laws, friction (static ≤ μsN, kinetic = μkN), tension in connected bodies, and the work–energy theorem with conservative potentials. Statics requires both ΣF = 0 and Σtorque = 0 about a cleverly chosen pivot. Rigid-body rotation needs moment of inertia, torque, angular momentum conservation, and rolling without slipping (v = ωR). Gravitation: Kepler's third law, orbital speed, and gravitational potential energy U = −GMm/r. Fluids: hydrostatic pressure, Archimedes' principle, continuity and Bernoulli.
Traps
- Mixing frames (accelerating lift, rotating platform).
- Forgetting that static friction adjusts to need up to a maximum.
- Applying energy conservation where friction does non-zero work.
- Confusing centre-of-mass motion with internal motion.
- In rolling problems, forgetting the rotational kinetic energy term.
Worked example
A block slides down a rough incline of angle θ, height h, coefficient μ. Energy: mgh − μmg cosθ·(h/sinθ) = ½mv². Solve v = √(2gh(1 − μ cotθ)). Rule of thumb: if the result under the root is negative, the block never reaches the bottom - check that first.