1. This is an animated derivation using polar coordinates that produces both the magnitude and direction of the centripetal acceleration on an object moving at constant speed around a circular path. To use it you will have to provide the narration. Best wishes, Leo Takahashi, The Pennsylvania State University, Beaver Campus

2. Centripetal Acceleration A derivation using Polar Coordinates

3. +y   R  +x = Cos + Sin = -Sin + Cos

4. +y V R +x V = v

5. = -Sin + Cos V = v( ) -Sin + Cos V = v = v(-Cos - Sin )

6. S  R = v(-Cos - Sin ) V = v

7. = (-Cos - Sin ) = v(-Cos - Sin ) = v(-Cos - Sin ) V2 = Cos + Sin V V - = - Cos - Sin

8. V2 = () - ac = v2/R

9. +y ac R +x ac = v2/R