Laws of Motion & Friction — 20 Core Concept Bullets — Summary

Newton's First Law: No net force → no acceleration. Inertia ∝ mass. Force is needed to CHANGE motion, not maintain it.
Newton's Second Law: F = ma = dp/dt. Dimension of force: [ $M^{1}$$L^{1}$$T^{-2}$ ]. Always apply to net force, not individual forces.
Newton's Third Law: F_AB = −F_BA. Forces act on DIFFERENT bodies, are simultaneous, equal in magnitude, opposite in direction.
N and mg on the same body are NOT an action-reaction pair — they are balanced forces. True pair: Earth pulls block (mg) ↔ block pulls Earth (mg).
Momentum p = mv [ $M^{1}$$L^{1}$$T^{-1}$ ]. Conserved when F_ext = 0 on the system.
Impulse J = F $\Delta t$ = $\Delta p$ [ $M^{1}$$L^{1}$$T^{-1}$ ]. Area under F–t graph equals change in momentum.
FBD is mandatory before applying F = ma. Draw it for every body separately.
Lift (upward acceleration): W' = m(g + a) → heavier. Lift (downward acceleration): W' = m(g − a) → lighter. Free fall: W' = 0.
Sign convention for lift: upward = positive. Be consistent throughout the solution.
Atwood machine: a = (m_{1} − m_{2})g / (m_{1} + m_{2}), T = 2m_{1}m_{2}g / (m_{1} + m_{2}). Always: m_{2}g < T < m_{1}g.
Static friction is SELF-ADJUSTING: 0 ≤ f_s ≤ μ_s N. It does NOT always equal μ_s N.
Compare F_applied with μ_s N first. If F < μ_s N, body stays still and f_s = F_applied.
Kinetic friction: f_k = μ_k N (constant). Rolling friction: f_r = μ_r N. Order: μ_s > μ_k >> μ_r.
On inclined plane: N = mg cos θ (not mg). Weight along incline = mg sin θ.
Angle of repose: tan θ = μ_s. At this angle, body is on the verge of sliding.
Centripetal force F_c = $mv^{2}$ /r is NOT a separate force — provided by friction/tension/gravity.
Level road: friction provides centripetal force. v_max = √(μrg).
Banked road (no friction): tan θ = $v^{2}$ /(rg). Design speed: v = √(rg tan θ).
Dimensional formula: Force [ $M^{1}$$L^{1}$$T^{-2}$ ], Momentum [ $M^{1}$$L^{1}$$T^{-1}$ ], μ [dimensionless].
True weight (mg) never changes with acceleration. Only APPARENT weight (normal force N) changes.