Is the Bottom Velocity of a Ferris Wheel Really Twice That of the Top?

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SUMMARY

The discussion centers on the misconception regarding the velocities of points on a Ferris wheel, specifically that the bottom velocity is twice that of the top. Participants clarify that while the top point has velocity v and the bottom point has velocity -v, the difference in velocities is 2v, but this does not imply that the bottom velocity is twice the top velocity. The mathematical demonstration reveals that both points have equal magnitudes of velocity, just in opposite directions, debunking the initial claim.

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I see in the description of non-uniform circular motion in a textbook, referring to a ferris wheel, that the velocity of an object at the bottom must be twice the velocity at the top, but it is not mathematically shown and it is not immediately obvious to me. Can someone show a simple mathematical demonstration of that?
 
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Are you sure that is what is said? If the point on top has velocity v, the point on the bottom must have the same speed but opposite direction so velocity -v. The difference in velocities is v- (-v)= 2v but it is NOT true that one is "twice" the other.
 

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