# Torsion pendulum

1. Oct 1, 2009

### reb659

1. The problem statement, all variables and given/known data
In the experiment, you will study an oscillator called a "torsion pendulum." In this case, the restoring "force" is the torsion constant of the wire that suspends the weight X and the inertial term is the rotational inertia of the suspended mass. You will compare the periods of a suspended sphere and of a suspended cube. The rotational inertia of a sphere is Is = 110msD2 where ms is the mass of the sphere and D is its diameter. The rotational inertia of a cube is Ic = 61mcS2 where mc is the mass of the cube and S is the length of its side. If the cube and the sphere are suspended from the same wire, what is the expected ratio of their periods, Tc/Ts?
Assume that D = S
ms = 020kg
and mc = 12 kg

2. Relevant equations

3. The attempt at a solution

I'm pretty lost with this one.

2. Oct 1, 2009

3. Oct 1, 2009

### willem2

I wonder why they gave those moments of inertia. the real values are

$$I_s = \frac { m_s d^2 } {10}$$

and

$$I_c = \frac { m_c s^2 } {6}$$

Do you know the solution of a simple harmonic oscillator?

$$F = m\frac {d^2x}{dt^2} = - k x$$

you don't know the torsion constant, but because you only need the ratio of the periods
that isn't a problem.