Finding angular acceleration from torque

Question

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.

Answer 1

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 $\tau = \frac{1}{2} MR^2\alpha$.)

Next, note that the moments of inertia of different parts of the windmill do add up to produce the total, just like with mass. You can't just use the moment of inertia of one propeller prop, you have to calculate the total moment of inertia.

Finally, consider this: what information can you get from the video, that could supplement the 3 "givens"? There's no length scale in the video, so you can't measure the length of a prop directly, but there is a time scale. What can you do with that?