Friction & Inclined Planes

Friction is a contact force that opposes the relative motion (or tendency of motion) between two surfaces.

Static friction (fₛ) acts when there is no relative motion. It adjusts up to a maximum value: fₛ(max) = μₛN.

Kinetic friction (fₖ) acts when surfaces slide. It is constant: fₖ = μₖN, and always μₖ ≤ μₛ.

On an inclined plane at angle θ: component of gravity along incline = mg sin θ, normal force N = mg cos θ.

A block stays stationary on an incline if tan θ ≤ μₛ. The angle of repose θᵣ = tan⁻¹(μₛ).

Friction does negative work on sliding objects, converting kinetic energy to heat.

In JEE problems, always draw a Free Body Diagram (FBD) and identify the direction of friction carefully.

Rolling friction is much smaller than sliding friction — this is why wheels are efficient.