How Does Halving the Radius Affect the Period in Centripetal Acceleration?

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Halving the radius in a centripetal acceleration scenario affects the period significantly. If the acceleration remains constant, the new velocity must be calculated to maintain the same centripetal force. The initial and final equations for acceleration and period show that the period decreases, but the exact factor depends on the new velocity after the radius is halved. The discussion emphasizes the importance of maintaining constant acceleration to accurately determine the new period. Understanding these relationships is crucial for solving centripetal acceleration problems effectively.
smillphysics
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What happens to the period when you cut the radius in half for a centripetal acceleration problem?


a=V^2/r
T=2pi*r/v


I need some background on this question. I believe the answer is the period is decreased by a factor of 2. I am just slightly confused.
 
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Well, that would depend. Are you keeping the acceleration on the body the same?
If so, then the problem isn't quite as trivial:
ainitial = v²/rinitial
afinal = u²/rfinal
Tinitial = 2πr/v
Tfinal = 2π(½r)/u

Since we want the acceleration before we cut the radius in half to be the same as after, all that remains to find u and Tfinal is a simple equation.
 

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