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

AI Thread Summary
The discussion focuses on calculating the period of oscillation for a compound pendulum consisting of a rigid rod and a meter stick using the parallel-axis theorem. The initial approach of using the simple pendulum formula was deemed inadequate, prompting a need to determine the moment of inertia (MI) of the combined system. Participants emphasized the importance of finding the MI about the pivot point to accurately compute the period. A breakthrough occurred when it was realized that the mass cancels out in the formula, allowing for the calculation without needing the mass value. The conversation highlights the relevance of understanding compound pendulums in solving such problems.
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[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?
 
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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.
 
It definitely doesn't give the mass, although I know you need it to find MOI. Does anyone know a way around this?
 
Never mind. I figured it out. Just put I into T=2(pi) sqrt(I/mgd) and the mass cancels out.
 
Good for you!
 

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