[started] 1/25/17


  • Direction: Opposes relative motion between two surfaces
  • Magnitude:
    • Kinetic friction f_k=\mu_k N
    • Static friction, matches external force up to maximum f_s \leq \mu_s N
  • Concept: Friction points opposite to relative velocity
  • Problem: A thin slab of mass m  rests centered on two cylinders of radius r rotating with angular velocity \omega  in opposite directions. What force F  is required for the slab travel with velocity v_0  across the cylinders? The coefficient of friction is \mu .


  • Concept: Reaction force angle
  • The reaction force R is the net force of friction f and the normal force N . The reaction angle \varphi=\arctan(\frac{f}{N}) is the angle between the reaction force and normal force. Once the interaction between two surfaces is determined, the reaction angle does not change.
  • Problem: A force F is applied at an angle \theta from the hortizontal to move a block across the ground wih constant velocity. At what angle is the force minimized? The coefficient of friction is \mu


  • Concept: Self-locking
  • Occurs when the applied force F  to displace an object contributes to the normal force N  and friction f . There is a critical angle \theta beyond which the object will not move no matter how much force is applied.
  • Problem: A rod of length l rests vertically on the ground. A rope is attached to the top end and the ground, making an angle \theta with the verticle. If a force F is applied horizontally on the rod, how far from the bottom does it need applied to be for the rod to self-lock? The coefficient of friction is \mu_0 .