# Homework Help: Metal disk problem!

1. Nov 29, 2012

### NasuSama

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

A uniform metal disk (M = 8.21 kg, R = 1.88 m) is free to oscillate as a physical pendulum about an axis through the edge. Find T, the period for small oscillations.

2. Relevant equations

$I = mr^{2}/4$
$T = 2\pi √(I/mgd)$

3. The attempt at a solution

I combined the formula together to get:

$T = 2\pi √((mr^{2}/4)/(mgr))$
$T = 2\pi √(r/(4g))$

2. Nov 29, 2012

### Staff: Mentor

How did you arrive at this result?

3. Nov 29, 2012

### NasuSama

I am thinking that I need to use the moment of inertia of the disk.

4. Nov 29, 2012

### Staff: Mentor

Of course you do, but that's not the correct formula.

5. Nov 29, 2012

### NasuSama

Then, it's something like I = mr²/2, rotating to its center. However, the disk oscillates through its edge.

I am not sure which path to go for...

6. Nov 29, 2012

### Staff: Mentor

Right.
Use the parallel axis theorem. (Look it up!)

7. Nov 29, 2012

### NasuSama

Hm.. By the Parallel Axis Theorem, I would assume that:

$I = I_{center} + md^{2}$
$I = mr^{2}/2 + mr^{2}$ [Since the disk rotates about an axis through the edge, we must add the inertia by mr². r is the distance between the center and the edge of the disk.]
$I = 3mr^{2}/2$

Is that how I approach this? Let me know where I go wrong. Otherwise, I can just plug and chug this expression:

$T = 2\pi √((3mr^{2}/2)/(mgr))$
$T = 2\pi √(3r/(g))$

8. Nov 29, 2012

### NasuSama

Nvm. My answer is right. Thanks for your help by the way!

9. Nov 29, 2012

Good!