Calculating Centripetal Force: Diagramming and Solving for X and Y Forces

[kdburns]

How would you go about proving that centripetal F=(mv^2)/r by diagramming and solving for the magnitude of the forces in the x and y direction?

For example, suppose I wanted to calculate the work done in the radial direction by centripetal force.

 

[A.T.]

http://en.m.wikipedia.org/wiki/Centripetal_force#Uniform_circular_motion

 

[kdburns]

Thanks so much! Really helpful

 

[daqddyo1]

Work is the product of the applied force magnitude x the magnitude of the displacement (D) in the same direction as the applied force. As a result, this is sometimes expressed as W = F x Dcosθ where θ is the angle between the two vectors (F and D). Since the F and D vectors are always perpendicular for circular motion of a mass at a constant speed, the angle between the two vectors is always 90°. So, the work done in circular motion at constant speed is 0 since cos90° is 0.