⚖️ Laws of Friction

• Friction opposes relative motion.
• Static friction is self-adjusting up to a limit.
• Kinetic friction is independent of velocity.
• μ is independent of apparent area of contact.

📐 Angle of Friction (λ)

tan λ = μ_s

Angle of repose (θ): tan θ = μ_s → the maximum incline at which a block just starts sliding.

Component of gravity: mg sinθ (down the plane), mg cosθ (normal).

If θ ≤ angle of repose: block at rest, f_s = mg sinθ

If θ > angle of repose: block accelerates down with a = g(sinθ – μ_k cosθ)

💡 NEET TIPS & SHORTCUTS

• When pulling/pushing a block, the normal force changes: if force is at an angle, N = mg – F sinθ (upward pull) or N = mg + F sinθ (downward push).
• For two blocks in contact, friction between them depends on relative motion tendency.
• Maximum static friction is the threshold; beyond that, kinetic friction acts.
• In circular motion on banked roads, friction provides part of centripetal force.

⚠️ COMMON MISTAKES

• Assuming kinetic friction equals static friction value.
• Forgetting that friction opposes relative motion, not the direction of motion of the body (e.g., a box on a moving belt).
• Using μ_s instead of μ_k once motion starts.
• Neglecting the effect of angle of applied force on normal reaction.

Static friction max: f_s,max = μ_s N

Kinetic friction: f_k = μ_k N

Angle of repose: tanθ = μ_s

Acceleration down incline: a = g(sinθ – μ_k cosθ)

Acceleration up incline: a = g(sinθ + μ_k cosθ)

Force to just move (horizontal): F = μ_s mg