Different Periods of Brass Rod and Ball on String

In summary, two objects of the same length (a brass rod and a brass ball attached by a string) have different periods when oscillating like a pendulum due to their different moments of inertia and the fact that gravity acts on their center of masses at different distances. Even if the center of mass were the same for both objects, their periods would still be different because the moment of inertia also plays a role. To calculate the period, one can use rotational dynamics. This may seem counterintuitive since gravity causes all objects to accelerate at the same rate, but the difference in moments of inertia accounts for the difference in periods.
  • #1
cragar
2,552
3
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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  • #2
Firstly, they have different moments of inertia. Secondly, yes, gravity acts at the center of mass which is different for the two systems.
 
  • #3
if I made the rod longer to where its center of mass was the same as the ball would they oscillate together?
 
  • #4
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".
 
  • #5
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.
 

1. What are the different periods of brass rod and ball on string?

The different periods of brass rod and ball on string are the time it takes for the ball to complete one full oscillation when it is attached to a brass rod and suspended with a string. These periods can vary depending on the length and thickness of the rod, as well as the mass of the ball.

2. How do you determine the period of a brass rod and ball on string experiment?

The period can be determined by measuring the time it takes for the ball to complete a certain number of oscillations, usually 10 or 20. This time can then be divided by the number of oscillations to calculate the period. It is important to use a stopwatch or timer with precision to get accurate results.

3. What factors affect the period of a brass rod and ball on string?

The period of a brass rod and ball on string can be affected by several factors, including the length and thickness of the rod, the mass of the ball, and the strength of the gravitational field. Other factors such as air resistance and friction can also have a small impact on the period.

4. How does changing the length of the brass rod affect the period?

Changing the length of the brass rod can have a direct effect on the period. As the length increases, the period also increases. This is because the longer the rod, the longer the distance the ball must travel to complete one oscillation, resulting in a longer period.

5. What is the relationship between the mass of the ball and the period?

The mass of the ball has an inverse relationship with the period. This means that as the mass of the ball increases, the period decreases. This is because a heavier ball requires more force to move and complete an oscillation, resulting in a shorter period.

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