Types of friction:

1. Static Friction ($f_s$):

• Acts when there is no relative motion between surfaces
• Self-adjusting: 0 <= $f_s$ <= $mu_s$ * N
• Direction: opposes TENDENCY of relative motion
• At the verge of motion: $f_s$ = $mu_s$ * N (maximum static friction)

2. Kinetic (Sliding) Friction ($f_k$):

• Acts when surfaces are in relative motion
• Constant: $f_k$ = $mu_k$ * N
• Direction: opposes relative motion
• $mu_k$ < $mu_s$ (kinetic < static coefficient)

3. Rolling Friction:

• Much smaller than sliding friction
• Usually negligible in JEE unless specified

Angle of Friction (lambda): tan(lambda) = $mu_s$ This is the angle the resultant of N and $f_{max}$ makes with the normal.

Angle of Repose (alpha): tan(alpha) = $mu_s$ The maximum angle of an incline at which a body remains stationary. Note: angle of repose = angle of friction.

Friction graph: As applied force increases from 0:

• Static friction increases linearly up to $f_{max}$ = $mu_s$*N
• At $f_{max}$, body begins to move
• Friction drops to $f_k$ = $mu_k$*N and remains constant