Different Periods of Brass Rod and Ball on String

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The discussion centers on the differing oscillation periods of a brass rod and a brass ball on a string, despite having the same length. The key factors influencing their periods are their moments of inertia and the positions of their centers of mass. Gravity acts on the center of mass for both objects, but the varying distances and moments of inertia result in different oscillation behaviors. Even if the center of mass were aligned, the distinct moments of inertia would still lead to different periods. Understanding these dynamics requires knowledge of rotational dynamics principles.
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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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