Example 4: A 20-lb. wheel is supported by a freely-rotating roller and the wall. Determine the moment required to initiate the rotation of the wheel and whether or not it is possible for the wheel to roll up the wall. The coefficient of friction at the wall is 0.25.

Solution:

We begin by drawing a free-body diagram of the wheel.

Equilibrium Equations:

For rotation to be initiated, the wheel must slip at point A, so

Because of this, the equilibrium equations become

Friction Equation

This results in a moment of

Is it possible for the wheel to roll up the wall before slipping?

To check this, set . This results in

and

M for rolling is greater than M for slipping, so the wheel will rotate in place and not roll up the wall.