Coefficient of friction

  • The coefficient of friction($\mu$) is the ratio of the friction force compared to the normal reaction.
  • That is:
\begin{align} \mu = \frac{Fr}{N} \end{align}
\begin{align} \therefore Fr = \mu N \end{align}
  • It can be found by finding the angle of repose($\theta_R$) (see below) in that:
\begin{align} \mu = \tan{\theta_R} \end{align}

Normal Reaction

  • This is the force that always acts perpendicular to the surface of the object.
  • It is a reaction to all the forces in that direction (see right for example)
  • In a general case (top picture), it can usually be found through
\begin{align} N = mg\cos{\theta} \end{align}


  • Friction can usually found using this value $Fr = \mu N$
  • It always opposes the direction of motion

NB: Be very careful that one does not treat the weight's sliding force ($mg\sin{\theta}$) as friction, nor ignore it.

Limiting friction

  • This is the frictional resistance just as the object is about to move.
  • It is what determines the angle of repose

Angle of Static Friction/Repose

  • The angle of static friction ($\phi_s$) is the angle to the normal reaction that the resultant of the Friction and the normal makes.
  • When the limiting friction is used, this angle is known as the angle of repose($\theta_R$) and will equal the angle of inclination($\theta$).