# Homework Help: Period of a Pendulum and moment of inertia

1. Apr 27, 2010

### Quincy

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

A holiday ornament in the shape of a hollow sphere with mass 1.0×10−2 kg and radius 5.0×10−2 m is hung from a tree limb by a small loop of wire attached to the surface of the sphere. If the ornament is displaced a small distance and released, it swings back and forth as a physical pendulum. Calculate its period. (You can ignore friction at the pivot. The moment of inertia of the sphere about the pivot at the tree limb is (5/3)MR^2.)

2. Relevant equations

T = 2Pi*(sqrt(I/mgL))

3. The attempt at a solution

This is the only formula I know for the period, but the problem doesn't give the value of L. Is there another formula for the period?

2. Apr 27, 2010

### vela

Staff Emeritus
You're given enough info to figure out what L is. Think about what exactly L is defined as. It's the distance between what two points?

3. Apr 27, 2010

### zachzach

I think it is saying that it is not hanging. It is attached by a loop. Draw a loop around the limb and then draw the ornament attached to the loop.

4. Apr 27, 2010

### tiny-tim

Hi Quincy!

(have a square-root: √ and a pi: π and try using the X2 tag just above the Reply box )
Then invent a formula!

Find the torque (moment) of the weight at a typical angle, and then use the formula τ = Iα to get an (approximately) shm equation.

5. Apr 27, 2010

### zachzach

Wouldn't you still need that distance for I?

6. Apr 27, 2010

### Quincy

Oops, I misread the problem, I was thinking it was attached to a wire with some length instead of a loop.