# Easy Rotational Motion Question

## Homework Statement

A grindstone has a moment of inertia of 1.6*10^-3 kg m^2. When a constant torque is applied, the flywheel reaches an angular velocity of 1200 rev/min in 15 s. Assuming it started from rest, find (a.) the angular acceleration; (b.) the torque applied; (c.) the angle turned through the 15 s; (d.) the work W done on the flywheel by the torque.

## The Attempt at a Solution

I'm having some issues with part (a).
I used ω = ω_0 + alpha*t
and solved for alpha
alpha = (ω-ω_0)/t
alpha = (1200 rev/min * (2 pi)/rev * 60 min/s)/15 s
I get alpha is about 30,159 1/s^2

I don't see what I'm doing wrong. Thanks for any help which you can provide me.

Related Introductory Physics Homework Help News on Phys.org
For part (a), you're on the right track. Because the applied torque is constant, this means that angular velocity increases linearly. This should allow you to work backwards using $\omega_{0} , \omega_{f} ,$ and $\Delta t$.

Your problem is in the calculations. You've got 60min/s, which is incorrect. It should be 1min/60s. See if that puts you closer to your expected value and then substitute it back in to check the validity of your answer by solving for $\omega_{f}$ from $\omega_{0} , \delta t ,$ and $\alpha$.

Doc Al
Mentor
alpha = (1200 rev/min * (2 pi)/rev * 60 min/s)/15 s
You messed up the conversion from rev/min to rad/sec.

ah i feel dumb thanks

for part (c) I used
θ = θ_0 + ω_0*t + (alpha*t^2)/2
θ = 1200 rev/min * (2pi)/rev * min/(60 s) * 15 s + (8.38 1/s^2 * (15 s)^2)/2 ≈ 2,828
which I guess is wrong because the answer is 942
I don't see what I'm doing wrong here, I checked that the units canceled out

Well the answer you derived is just about 3x the answer the book gives you. See if you can find where you might have accidentally multiplied something by 3 (or got a constant 3x its correct value or forgotten to divide by 3. Your approach looks right as best I can tell so just double check your inputs and whatnot.

I have checked it and can't seem to find anything wrong with it, yet the answer is wrong.

Hmm. I can't think of what might be the issue. Maybe try integrating over the specified time interval and using your known initial values and whatnot? I don't know why that would change since your alpha is constant, but it couldn't hurt. Beyond that, I can't think of anything other than just making sure you're using the right values everywhere.

Doc Al
Mentor
for part (c) I used
θ = θ_0 + ω_0*t + (alpha*t^2)/2
θ = 1200 rev/min * (2pi)/rev * min/(60 s) * 15 s + (8.38 1/s^2 * (15 s)^2)/2 ≈ 2,828
which I guess is wrong because the answer is 942
I don't see what I'm doing wrong here, I checked that the units canceled out
For one thing, it starts from rest so ω_0 = 0.

Ya I don't think integrating is needed because the angular acceleration is constant. And ya I checked to make sure all my values were correct and they appear to be. Do you think the supplied answer is wrong?

For one thing, it starts from rest so ω_0 = 0.
thanks

Derp. I can't believe I missed that too!