Different Periods of Brass Rod and Ball on String

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Discussion Overview

The discussion revolves around the oscillation periods of a brass rod and a brass ball attached by a string, both of the same length, when released as pendulums. Participants explore the factors influencing their different periods, including moments of inertia and the positions of their centers of mass.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the different periods may be due to the different positions of the centers of mass of the rod and the ball.
  • Another participant points out that the moments of inertia of the two objects are different, which also affects their oscillation periods.
  • A question is raised about whether making the rod longer to align its center of mass with that of the ball would result in them oscillating together.
  • It is noted that the periods depend on moments of inertia, not solely on the centers of mass.
  • One participant expresses confusion about the dependence on moment of inertia, arguing that if the centers of mass are the same, they should fall together due to gravity acting uniformly.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are competing views regarding the influence of moments of inertia versus the positions of the centers of mass on the oscillation periods.

Contextual Notes

Some assumptions about the systems, such as the effects of gravity and the definitions of moments of inertia, are not fully explored or resolved in the discussion.

cragar
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Lets say I have a brass rod of length L, and then a brass ball attached by a string so that both objects are the same length, the brass rod and the ball on a string have the same length.
Now i will pull them back to the same point an let them oscillate like a pendulum. Why do they have different periods? Their centers of masses are at different places, is this the reason why?
Is gravity acting on their center of masses over different distances? And they are both allowed to rotate from the top of their frame.
 
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Firstly, they have different moments of inertia. Secondly, yes, gravity acts at the center of mass which is different for the two systems.
 
if I made the rod longer to where its center of mass was the same as the ball would they oscillate together?
 
The periods depend on their moments of inertia, not just their centers of mass. If you want to calculate the period just google something like "rotational dynamics".
 
okay why would it depend on their moment of inertia, If their center of masses are the same and gravity makes all things accelerate at the same rate it seems like they would fall together. It just seems weird to me.
 

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