# Rotational Forces on a Hollow Cylinder

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1. Oct 21, 2015

### Ben Reynolds

1. The problem statement, all variables and given/known data
I am trying to model a hollow cylinder of known radius r, length l and density rho.
The cylinder is fixed on a horizontal axle along its longest axis (l) and will have a force F applied tangentially to its surface and perpendicular to its axis, with negligible frictional forces acting between it and the axle.
What equations could I use to model the speed of its rotation?

2. Relevant equations
Mass = pi*r2*l*rho
Some equation involving moments, potentially?
I am a mathematician and have little work on angular velocity, so I apologise for the trouble.

3. The attempt at a solution
I have attempted to find a relevant equation but all searches gave either inapplicable scenarios or equations quoted ad verbatim with no clarification to notation.

2. Oct 21, 2015

### haruspex

Do you know about moment of inertia... how it is defined, the formula for the MoI of a cylinder, its use in angular acceleration...?

3. Oct 21, 2015

### Ben Reynolds

Okay, so I have found the equation I = MR^2 for a cylindrical shell of negligible width being rotated along its long axis, which is close to what I'm looking for. However, I would not know how to include such an equation in finding angular acceleration.

4. Oct 21, 2015

### haruspex

It's very like the linear equation: torque about axis = moment of inertia about axis * angular acceleration about axis.

5. Oct 22, 2015

### Ben Reynolds

That's perfect, thanks!