# Rectangular Disk with Circular Hole Period Question

1. Jan 14, 2012

### JohnnyCollins

1. The problem statement, all variables and given/known data
A circular disk with a rectangular hole has a radius of 0.620 m and mass of 0.470 kg. It is suspended by a point on its perimeter as shown in the figure. The moment of inertia about this point is I_p = 1.60E-1 kgm2. Its center of mass is located at a distance of s=0.120 m from the center of the circle as shown. If the disk is allowed to oscillate side to side as a pendulum, what is the period of oscillations

2. Relevant equations

ω=2∏f
f=1/T
I_g=1/2mr^2

3. The attempt at a solution
I'm lost on this question, any help would be greatly appreciated!

2. Jan 14, 2012

### Simon Bridge

Since you are stuck - go back to first principles ... start by drawing a free-body diagram for an arbitrary angular displacement and work out the torques. Fortunately you have been given the moment of inertia and the center of mass. Make an approximation for small angles and solve for T.

Last edited: Jan 14, 2012
3. Jan 14, 2012

### JohnnyCollins

So i took your advice and used the formula T=2∏√I/(mgd) and used 0.120 m for my distance, but I still ended up with the wrong answer. Am I on the right track ?

4. Jan 14, 2012

### Simon Bridge

d, in your formula, is the distance from the pivot to the center of mass.
0.120m is the distance from the center of the circle to the center of mass.
spot the difference.

5. Jan 14, 2012

### JohnnyCollins

Got it, thanks a lot for your help!

6. Jan 14, 2012

### Simon Bridge

No worries.

When you get stuck - go back to first principles and do a derivation.
It's amazing how naive you can be about this and still get results - just "describe the system in math and then fiddle the math" is very powerful.

In the process you may discover that you could have used a short-cut ... but having gone back over the basics deepens your understanding of the process.
Happy hacking.