How Does the Parallel-Axis Theorem Affect Pendulum Oscillation Periods?

[GreenLantern674]

[SOLVED] Pendulum Oscillations Problem

A very light rigid rod with a length of 0.500 m extends straight out from one end of a meter stick. The stick is suspended from a pivot at the far end of the rod and is set into oscillation.
(a) Determine the period of oscillation. (Hint: Use the parallel-axis theorem)
(b) By what percentage does the period differ from the period of a simple pendulum 1.00 m long?

I tried solving for period by using t=2(pi) sqrt(L/g) but that didn't work. It says to use the parallel axis theorum but I don't know what to do once I find I. Also, I don't think I can solve the second part until I get the first period, but once I do that would it just be T=2(pi) sqrt(L/g) for the period of the pendulum with 1m length?

 

[Shooting Star]

I think that the mass of the meter stick has to be given. Check for that.

Basically, you have to treat the light rod and meter scale as a compound pendulum. You have to find the MI of the rod+scale using parallel axis theorem. If you know the MI of the scale about one end, then you can find the MI about the pivot.

Read up a bit on compound pendulum or Kater's pendulum.

 

[GreenLantern674]

It definitely doesn't give the mass, although I know you need it to find MOI. Does anyone know a way around this?

 

[GreenLantern674]

Never mind. I figured it out. Just put I into T=2(pi) sqrt(I/mgd) and the mass cancels out.

 

[Shooting Star]

Good for you!