Laws of Motion & Friction — 5-Point Rapid Revision — Summary

Newton's Laws: First = inertia (no F → no a); Second = F = ma = dp/dt [ $M^{1}$$L^{1}$$T^{-2}$ ]; Third = F_AB = −F_BA on different bodies. N and mg on same body ≠ action-reaction pair.
Lift: Accelerate up → W' = m(g+a) heavy; down → m(g−a) light; free fall → W' = 0 (weightlessness).
Atwood: a = (m_{1}−m_{2})g/(m_{1}+m_{2}); T = 2m_{1}m_{2}g/(m_{1}+m_{2}); verify m_{2}g < T < m_{1}g.
Friction: Static is self-adjusting (0 to μ_s N — NOT always μ_s N); kinetic = μ_k N (constant; μ_k < μ_s). Incline: N = mg cos θ. Angle of repose: tan θ = μ_s.
Circular motion: F_c = $mv^{2}$ /r provided by real forces. Level road: v_max = √(μrg). Banked road: tan θ = $v^{2}$ /(rg).