# Finding angular acceleration from torque

We have to analyze this video

Givens:

• An applied net torque due to the wind on the windmill is equal to 1500 N*m.
• Each (of the 3) propeller props weighs approximately 45 Kg and has a Moment of Inertial equal to about 65% of that of a rod of the same mass being spun about its end.

• This torque is applied for approximately 45 seconds before the explosion, prior to which the windmill was at rest.

Question: What was the angular acceleration caused by the torque?

So here's my attempt at it: T=Ia (a is alpha) T=ML^2/3 * a * .65 (due to the whole 65% thing. Actually not sure if I should put 3*M for each propeller)

And so this is where I get stuck. I'm not given L, so I'm not sure how to work around this. I could also use $T=1/2MR^2\times a$, but then I dont know R.

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Thanks for marking this as homework; I'm sure someone will be able to give you hints. (I would myself, but it's rather late here!) –  Noldorin Nov 4 '10 at 1:08
Maybe I haven't understood the problem, but have you looked at en.wikipedia.org/wiki/List_of_moments_of_inertia (particularly to the rod with the axis of rotation at the end of the rod)?. That's according to your point 2). For using that equation, you need the angular momentum, however, you know the torque and you know the time in which the torque is being applied. As far as I can see, that's all the information that you need to calculate the angular acceleration. –  Robert Smith Nov 4 '10 at 1:54
@Robert Smith I think you're mistaking the L in that equation for angular momentum, when it's actually length of the rod. –  ZachMcDargh Nov 4 '10 at 2:31
@ZachMcDargh: Argh, you're so right. –  Robert Smith Nov 4 '10 at 4:15
Very strange that they chose to call that L. I was confused both by the OP's post and that equation on Wikipedia for a second. –  ZachMcDargh Nov 4 '10 at 4:49

The first thing I would point out to you is that $\tau = \frac{1}{2} MR^2 \alpha$ is really just $\tau = I\alpha$, with a particular choice of $I$. Is that choice appropriate for this problem? (Ask yourself the same thing any other time you consider using $\tau = \frac{1}{2} MR^2\alpha$.)