Moment of Inertia: Solve for Ft & Alpha

[epidote6]

I'm more having a problem of what they actually want and what I can use/assume. The question is:

A horizontal disk of moment of inertia I rotates frictionlessly around its axis. A massless pulley of radius r which shares the axis of rotation is attached to the disk. A massless string is wound around the pulley, passed over another massless frictionless pulley, and attached to a hanging mass m.

There are two pictures, one of a rotating disk from above with Ft pointing out from it. And the second of a hanging mass from the side with Ft pointing up and mg pointing down from the mass.

a) write down equation of motion for rotating disk. Denote angular acceleration by alpha.

I just have F(tension) = I * alpha. I think that's all it is.

b) Write down the equation of motion for the hanging mass. Its acceleration a is related to ang acc. of disk by a = r*alpha.

Do I just plug in a/r for alpha?

C) Solve equations for a) and b) for Ft and alpha. (Express answers in terms of known quantities, namely, I, r, m, and g.)

This is the one I am confused about since for b) i don't have an alpha. Also isn't Ft = mg ? Maybe I am making this harder that it actually is. All my other problems were a lot harder for this to be as simple as I have it.

I appreciate the help.

 

[mathmike]

can u post a pid of the prob

 

[Diane_]

I presume you've already studied linear motion. Pretty much everything you studied there has an analog in rotational motion, and you can use the understanding you gained there to help you here.

For instance: the angular acceleration alpha is analogous to the linear acceleration a, with the relationship between them being given by the equation you cite. Consider your first problem: would you know what to do if you were asked to write the equation of motion for a particle moving under acceleration x? You're going to do the same thing here, using the rotational analogues. One equation that you almost certainly know is the expression for Newton's Second Law: F = ma. You have written that you have F = I*alpha. Think about this for a second: you have a linear quantity on the left and angular quantities on the right. That can't be correct. Can you think what the angular analog for force would be? That's what should be on the left. Once you know that, you should be able to rewrite your equation correctly by using the relationship between force and its angular analogue.

I know this is a little vague, but this is a fairly simple problem and I'm having a hard time giving you hints without actually telling you the answer. Look it over and let me know if it helps or if you have further questions.

 

[epidote6]

Ahh, I should have known that. Need to use torque

 

[Diane_]

Nicely done. :)