Applying work energy theorem to unifrom circular motion

[Vriska]

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

 

[Doc Al]

In uniform circular motion, the force and displacement are always at right angles--no work is done.

 

[kuruman]

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.