Question on rotational dynamics

1. Oct 31, 2004

mathlete

Here is the question (it's part of a lab):

"From your lectures in mechanics you should be able to derive:
$$\alpha = \frac{mgr}{I+mr^2}$$
This equation ignores the effect of the pulleys and the mass of the connecting string"

The lab was basically setting up a mass on a string over a pulley, connected to a rotation horizontal disc which would oscillate back and forth (if this information is needed).

Don't know where to start - I thought maybe conservation of energy, PEi + KEi = PEf + KEf, but I can't get anywhere.

2. Oct 31, 2004

Sirus

What is the question? Do they want you to derive that equation?

3. Oct 31, 2004

mathlete

Yes, that was the whole question. Don't know what to do..

4. Nov 1, 2004

mathlete

Anyone have an idea?

5. Nov 1, 2004

arildno

Since you haven't bothered with the simple courtesy of defining your terms, nope.

6. Nov 1, 2004

mathlete

If you dont know that I is moment of inertia and m is mass, you probably can't answer it anyway.

7. Nov 1, 2004

I of what?
m of what?
r of what?

8. Nov 1, 2004

arildno

For what it's worth, here's your solution:
The magnitude of yhe string's acceleration is related to the disk's angular acceleration by:
$$|a|=r\alpha$$
where the ang. acc. is considered greater than zero.
Hence, the tension in the rope is given by:
$$T=mg-mr\alpha$$
Hence, the momwnt-of momwntum wquation about the disk's center is:
$$mgr-mr^{2}\alpha=I\alpha$$

Next time, show a proper measure of respect towards your readers than some muddøed half-baked account of an experiment..:grumpy:

9. Nov 1, 2004

mathlete

I was just reading the problem straight from the book, verbatim. Thanks for the answer though

10. Nov 1, 2004