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: