Derivation of a = v2/r

L

Lindsey

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Can anyone please tell me how the formula for centripetal acceleration (a=v2/r) is derived?
 

Doc Al

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You should be able to find this in any number of physics books. In any case, the basic idea is this:

An object in circular motion has at any point a tangential speed V= (omega)r. To find the acceleration, take two points separated by d(theta). Draw the vectors representing these two velocities. The difference between them (which points towards the center) is dV = Vd(theta). The acceleration a = dV/dt = Vd(theta)/dt = V(omega)= V(V/r) = V2/r.

Hope this helps a little.

Just to be clear: omega is the angular speed, V is linear speed.
 
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