A hollow cylinder (radius $R$) is rolling against the wall at angular speed $\omega$. The coefficient of friction between the cylinder and the wall(ground) is $\mu$. After how many rotations the cylinder will stop rotating?

So I figured I need to find the time taken for cylinder to stop moving, and that would be

$$

\beta=-\omega/t => t = -\omega/\beta

$$

Where $\beta$ is angular acceleration, which is known from torques:

$$

2*F_f*R = I*\beta

$$

That's where I got stuck… How do I know the friction? I'm familiar with such equation:

$$

F_f = \mu*F_n

$$

How do I find the normal force? Does it have anything to do with centripetal force?

## Best Answer

Hint:Look at the following diagram, and then solve the equations:Or just notice that $F_w$ and $F_f$ do not depend on $\omega$, then use the Work-Energy principle.

step by step solution: