Calculate Force for Rotating a Cylinder: Mass and Diameter Guide

[pitchharmonics]

Given that you know the mass and diameter of a cylinder, what step do I need to take to figure out the force needed to rotate the cylinder.

All I can figure is that I multiply the mass times gravity.. please help

 

[FancyNut]

hmm I'm not sure but I think you need to calcuate the cetripetal acceleration which is $$\frac {v^2}{r}$$ or $$w^2 r$$ where w is omega the angular velocity.

$$\sum F_r = m a_r = \frac { m v^2}{r}$$

Do you know the velocity and radius?

EDIT: oh you said you know the diameter so the radius is just that divided by 2. Now you need to know the velocity.

 

[pitchharmonics]

there's no velocity but constant acceleration exists.

 

[FancyNut]

I meant tangential or angular velocity... Maybe you could get those in terms of mass and radius? Isn't there any more info? Like the time is takes for the cylinder to make a full circle?

 

[Sirus]

How is the cylinder positioned with respect to the axis of rotation (i.e. rotate it about what axis?)?

 

[pitchharmonics]

the cylinder is rotating counterclockwise, the axis of rotation is located at the center of the cylinder and expands out to its full diameter, I assume it is rotating about the z axis.

 

[Sirus]

You know that the net torque acting on the cylinder can be expressed as follows:
$$\sum \tau=I\alpha$$
where I is the moment of inertia of the cylinder around an axis passing through its center of mass, and alpha is angular acceleration.
So: $$F_{net}~r=\frac{1}{2}mr^{2}\alpha$$
$$F_{net}=\frac{1}{2}mr\alpha$$
Assuming no friction is present, the applied force is the net force. You can also convert this to include tangential acceleration rather than angular if needed.

 

[BobG]

Sirus has the right idea. Don't they tell you what the angular acceleration should be, though? Technically, any angular acceleration above zero will rotate the cylinder, which means any force above zero will rotate it eventually.

Moment of Inertia for various shapes can be found by integration. You can also find simplified equations for moment of inertia at various sites, such as:

http://scienceworld.wolfram.com/physics/MomentofInertia.html (There's a table if you scroll down the screen).

Mutliplying the moment of inertia by the angular acceleration gives you torque. Torque is also equal to force times the radius (at least for a cylinder, technically torque is force times radius times the sine of the angle between the force vector and the radius vector - in this case, the angle is 90 degrees). So, to get the force, you need to divide the radius back out of your torque.