Mechanics
Core concepts
Mechanics questions rest on Newton's three laws, the impulse–momentum theorem, conservation of linear and angular momentum, work–energy relations, and rotational analogues of translational quantities. You should be fluent in resolving forces on inclines, handling tension in connected bodies, and applying the parallel-axis theorem for moments of inertia. Uniform circular motion and centripetal force appear frequently, as does projectile motion with independent horizontal and vertical components.
Traps candidates fall into
- Confusing mass with weight, or forgetting that normal force is not always equal to mg on an incline or in a lift.
- Applying conservation of momentum to systems with external impulses, such as friction or a fixed pivot.
- Treating angular velocity as constant when torque acts, or mixing up angular and linear acceleration via a = rα (valid only for rolling without slipping).
- Assuming a collision is elastic when the problem only says the bodies stick together.
Rule of thumb
Always draw a free-body diagram before writing equations, and check units dimensionally. For a body on a rough incline, the condition for sliding is tan θ > μ.
Worked example
A 2 kg block slides down a 30° incline of length 5 m with μ = 0.2. Component of gravity along the slope: mg sin30° = 2×9.8×0.5 = 9.8 N. Friction: μmg cos30° = 0.2×2×9.8×0.866 ≈ 3.39 N. Net force ≈ 6.41 N, so acceleration ≈ 3.2 m/s². Velocity at the bottom from v² = 2as gives v ≈ 5.66 m/s.