Friction

#### 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}

(2)
\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

- 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($\theta$).

page revision: 1, last edited: 04 Oct 2011 12:04