Applying work energy theorem to unifrom circular motion

AI Thread Summary
The discussion focuses on deriving the equation for centripetal acceleration using the work-energy theorem. It begins by considering the displacement in uniform circular motion and applying the theorem, leading to an equation involving force. However, a critical error is identified: in uniform circular motion, the force and displacement are perpendicular, resulting in no work being done. Additionally, the treatment of kinetic energy as a vector is incorrect, as kinetic energy is a scalar quantity. The conclusion emphasizes the need to correctly apply the principles of physics to avoid misconceptions in circular motion dynamics.
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Homework Statement


attempt to derive the equation of centripetal acceleration using work energy theorem

Homework Equations



work done = Change in kinetic energy

The Attempt at a Solution



consider diametrically opposed points occurring in uniform circular motion - displacement = 2*R and let force be denoted by F

By work energy theorem ; F*2R = 1/2mv^2 - (-1/2mv^2)
F = mv^2/2R

...
So close...
Where did I go wrong
 
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In uniform circular motion, the force and displacement are always at right angles--no work is done.
 
Also, kinetic energy is not a vector. It is incorrect to say that kinetic energy is positive when the mass is moving in one direction and negative when moving in the opposite direction.
 
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