Must-Know Before NEET

Work

• W = Fd cos θ; positive (θ < 90°), zero (θ = 90°), negative (θ > 90°)
• W = 0 for: centripetal force, normal force on level surface, gravity on horizontal motion
• Variable force: W = area under F-x graph

Energy

• KE = ½$mv^{2}$ = $p^{2}$/(2m); always ≥ 0
• PE_gravity = mgh; PE_spring = ½$kx^{2}$
• Work-Energy Theorem: W_net (ALL forces) = $\Delta K$E — ALWAYS valid

Conservation

• Mechanical energy (KE + PE) conserved ONLY when no non-conservative forces act
• Friction converts mechanical energy to heat (non-conservative)
• Total energy always conserved (including heat)

Power

• P = W/t = Fv cos θ; 1 hp = 746 W; 1 kWh = $3.6 \times 10^{6}$ J

Vertical Circular Motion

• String: top = √(gR), bottom = √(5gR); T_b − T_t = 6mg
• Rod: top = 0, bottom = √(4gR)
• At top (string): T = $mv^{2}$/R − mg (minimum T = 0 at v = √(gR))

Collisions

• Momentum ALWAYS conserved
• KE conserved ONLY in elastic (e = 1)
• Perfectly inelastic: bodies stick (e = 0), KE loss = m_{1}m_{2}u_r$el^{2}$/[2(m_{1}+m_{2})]
• Equal mass elastic: velocities exchange
• Equal mass perfectly inelastic: v_f = u/2; 50% KE loss

NEET Traps

1. Rod top speed ≠ √(gR) — it is ZERO
2. KE after inelastic ≠ 0 (unless total momentum = 0)
3. W_net ≠ W_applied (must add W_friction on rough surfaces)
4. Doubling speed → KE quadruples (not doubles)