# Question on rotational dynamics

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.

## Answers and Replies

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

Sirus said:
What is the question? Do they want you to derive that equation?
Yes, that was the whole question. Don't know what to do..

Anyone have an idea?

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

arildno said:
Since you haven't bothered with the simple courtesy of defining your terms, nope.
If you dont know that I is moment of inertia and m is mass, you probably can't answer it anyway.

arildno
Homework Helper
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I of what?
m of what?
r of what?

arildno
Homework Helper
Gold Member
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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:

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

arildno