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

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Homework Help Overview

The discussion revolves around a pendulum oscillation problem involving a rigid rod and a meter stick, specifically focusing on the application of the parallel-axis theorem to determine the period of oscillation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the use of the parallel-axis theorem to find the moment of inertia (MI) for the compound pendulum setup. Questions arise regarding the necessity of the mass of the meter stick and how to proceed without it. There is also discussion about the relationship between the periods of different pendulum lengths.

Discussion Status

The discussion is active, with participants questioning the information provided and exploring the implications of the parallel-axis theorem. Some guidance has been offered regarding the calculation of the moment of inertia, and one participant has indicated they found a way to proceed with the calculations despite the missing mass information.

Contextual Notes

There is a noted absence of the mass of the meter stick, which is critical for calculating the moment of inertia. Participants are considering how this impacts their ability to solve the problem.

GreenLantern674
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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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