# Angular Momentum of a flywheel problem

1. Mar 8, 2008

### Seraph404

1. The problem statement, all variables and given/known data

The angular momentum of a flywheel having a rotational inertia of 0.140 kg m$$^{2}$$ about its central axis decreases from 3.00 to 0.800 kg m$$^{2}$$/s in 1.50 s. a) What is the magnitude of the average torque acting on the flywheel about its central axis during this period? b) Assuming a constant angular acceleration, through what angle does the flywheel turn?

2. Relevant equations

$$\tau$$ = I$$\alpha$$ ?

3. The attempt at a solution

a) Part a is easy. Torque equals final momentum minus initial momentum over the time. The answer is -1.47 N

b) Part b is what I need help with. As a hint, what equations should I look at or try to combine?

Last edited: Mar 8, 2008
2. Mar 8, 2008

### Staff: Mentor

Find the angular acceleration, then use kinematics to find the angle.

3. Mar 8, 2008

### Seraph404

Well, I thought of that, but then how do I find angular velocity?

4. Mar 8, 2008

### Hootenanny

Staff Emeritus
Using kinematics as Doc Al said. You know that,

$$\alpha = \frac{d^2\theta}{dt} = \frac{d\omega}{dt}$$

Can you take the next step?

5. Mar 8, 2008

### Seraph404

Uh.. I'm still not getting 20.4 rad, for some reason.

Last edited: Mar 8, 2008
6. Mar 8, 2008

### Hootenanny

Staff Emeritus

7. Mar 9, 2008

### physixguru

Answers are not important if ya know the correct approach.

I hope my great colleagues above would agree.

Now for the help part..

Torque is the rate of change of angular momentum.
Next, torque= M*I * alpha
alpha=omega/t or omega= alpha*t
next, omega * time= angular displacement.
finally... angular displcement is what ya want .rest is easy.

Last edited: Mar 9, 2008