Laws of Motion
Laws of Motion turns Newton's three laws into problem-solving: free-body diagrams, friction, circular motion and momentum conservation.
Core rules
- First law defines inertia; second law F = dp/dt = ma for constant mass; third-law pairs act on different bodies, so they never cancel on one body.
- Impulse J = FΔt = Δp.
- Friction: f(s) ≤ μ(s)N and f(k) = μ(k)N. Friction opposes relative slipping, not motion in general.
- On an incline, a body sliding down has a = g(sinθ − μcosθ).
- Circular motion: a(c) = v²/r; banking angle tanθ = v²/rg; maximum safe speed on a level road v = √(μrg).
- Momentum is conserved when the net external force is zero; the rocket equation follows from variable mass.
Worked example
A curve of radius 100 m is banked for 20 m s⁻¹ with g = 10 m s⁻². Then tanθ = v²/rg = 400/(100 × 10) = 0.40, giving θ ≈ 22°. At exactly this speed no friction is needed; at higher speeds friction must act down the slope, so with μ > 0 the maximum safe speed exceeds 20 m s⁻¹.
Traps
Drawing action and reaction on the same free-body diagram; using μN as the friction force when the body is at rest and the required friction is smaller; treating centripetal force as an extra force rather than a resultant.