Simple rotational motion point problem

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In a discussion about a rotating disk with two points, it is established that point B is twice as far from the axis as point A. The linear speed of point A is confirmed to be slower than that of point B, but the initial guess of V/4 for point A's speed is incorrect. The distance from the center to point A is R, while point B is at 2R, leading to the conclusion that both points complete one rotation in the same time. The correct relationship between their speeds is clarified, emphasizing that point B travels a greater distance in the same time frame. The conversation focuses on understanding the principles of rotational motion and the relationship between linear speed and distance from the axis.
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Two points are on a disk that rotates about an axis perpendicular to the plane of the disk at its center. Point B is 2.00 times as far from the axis as point A.

If the linear speed of point is V, then the linear speed of point A is

I know the speed of A must be less and i think its V/4. Is this right?
 
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Yes, it is slower, no, it not V/4.

Suppose the distance from the center of the disk to point A is R so the distance from the center to point B is 2R. How far does each travel in one rotation? Remember that the both complete one rotation in the same time.
 
ok. i think its V/2?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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