# Inertia and Torque given Angular Velocity

1. Nov 8, 2010

### Lucidity

1. The problem statement, all variables and given/known data

A rotor of moment of inertia IR and outer radius R spins about a vertical axis. The rotor mount is not friction free. Rather, there is a small constant friction torque of magnitude τf . A string of negligible mass is wound around the outside of the rotor. The string is attached to the rotor in a way that allows it to come free when the end is reached. The other end of the string is attached to a weight of mass m hanging from a massless frictionless pulley. When the system is released from rest the angular velocity of the rotor increases linearly at a rate α1 under the influence of the tension in the string and the torque due to friction. After the string detaches from the rotor, the rotor’s angular acceleration becomes α2 (a negative quantity) due to the friction torque.

Find expressions for I0 and τf in terms of some or all of the quantities α1, α2, m, R, and g the acceleration of gravity.

2. Relevant equations
I=mR^2
τ=Iα

3. The attempt at a solution
For inertia, would it simply be mR^2? I remember something about a parallel line to the axis of rotation, involving a cross product and all of that... mR^2 seems too easy to be correct...
but if inertia = mR^2, would τ simply be mR^2(α1-α2)?
The τ equation doesn't sound right at all, and I'm somewhat confused on what to do here.

Thanks!

2. Nov 14, 2010

### issacnewton

what is I0 ?

3. Nov 15, 2010

### kungfujew92

OP, do you go to MIT by chance?