Laws of Motion
What this domain tests
Newton's three laws, impulse and momentum conservation, friction on level and inclined surfaces, circular motion and banking, and simple pulley and contact problems.
Core rules
- First law defines inertia; second law F_net = ma = dp/dt; third-law pairs act on different bodies and never cancel on a single body.
- Impulse FΔt = Δp; total momentum is conserved when no external force acts - recoil, explosions, collisions.
- Static friction is self-adjusting up to f_s(max) = μ_sN; kinetic friction f_k = μ_kN with μ_k usually less than μ_s.
- On an incline, N = mg cosθ, so the friction term uses cosθ too.
- Circular motion needs a centripetal force mv²/r: string tension, friction on a level road, or N sinθ on a banked road where tanθ = v²/rg.
- In a lift, apparent weight N = m(g ± a).
Worked example
A 5 kg block slides down a 30° incline with μ = 0.2, taking g = 10 m/s². Find its acceleration. Driving component mg sinθ = 5 × 10 × 0.5 = 25 N. Friction μmg cosθ = 0.2 × 5 × 10 × 0.866 = 8.7 N. Net force = 16.3 N, so a = 16.3/5 ≈ 3.3 m/s². Dividing symbolically gives a = g(sinθ − μcosθ), showing that the mass cancels.
Traps that cost marks
- Adding an action–reaction pair on the same body and concluding the net force is zero.
- Using N = mg on an incline or inside an accelerating lift.
- Applying the coefficient of static friction after sliding has begun.
- Sign errors when using tanθ = v²/rg for banked roads.