Error Analysis — Common Mistakes in Laws of Motion — Notes

#	Common Error	Why It's Wrong	Correct Approach
1	Treating N and mg as action-reaction pair	They act on the SAME body (the block); A-R pairs act on different bodies	True A-R pair: Earth pulls block (mg) ↔ block pulls Earth (mg upward)
2	Assuming f_s = μ_s N always	Static friction is self-adjusting; f_s = μ_s N only at limiting condition	Compare applied force with μ_s N first; if F_applied < μ_s N, then f_s = F_applied
3	Using N = mg on an inclined plane	On an incline, N balances mg cos θ, not mg	Always resolve weight: N = mg cos θ
4	Forgetting μ_k < μ_s	Students sometimes use μ_s for kinetic friction after motion begins	Once sliding, use f_k = μ_k N
5	Wrong sign in lift problems	Mixing up directions; treating downward acceleration as adding to g	Fix sign convention: upward positive always. W' = m(g + a) up, m(g − a) down
6	Missing centripetal force source	Writing "centripetal force" as a separate force in FBD	Centripetal force is provided BY real forces (friction, tension, gravity) — not an extra force
7	Atwood: forgetting T is same throughout string	Students sometimes assign different tensions to each side	For massless string over frictionless pulley, tension is uniform throughout
8	Momentum conservation when friction acts	Applying conservation of momentum when friction (external force) is present	Conservation of momentum requires F_ext = 0 on the system
9	Confusing impulse and force	Using F = J/t without considering if force is constant	J = ∫F dt = $\Delta p$ ; only equals F· $\Delta t$ for constant force
10	Wrong component in circular motion	Using mg instead of N or f as centripetal force depending on context	Identify what physical force provides centripetal force in each scenario