I would like to put this into a differential equation. This is what I have.
$$r \times F = I \ddot\theta + \mu \dot\theta + k \theta$$
What I need verified:
- $\text{Torque} = I\ddot\theta + \mu \dot\theta + k \theta$
- $I$ = moment of inertia (constant)
- $\mu$ = kinetic friction (constant)
- $k$ = spring constant ( in my application it will be 0 ) (constant)
- $\theta$ = rotation (function)
- Torque = $r F$
- $r$ = radius
- $F$ = force
- It's safe to set the two equations for Torque equal to describe the system.
- That a solution to the differential for $\theta(t)$ will describe the rotation with respect to time of the circle cylinder.
Any insight would be much appreciated, thanks.