1. To use it you will have to provide the narration.
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. V = v
= -Sin + Cos
V = v( )
-Sin + Cos
= v(-Cos Sin )

6. = v(-Cos Sin )  R S V
= v

7. - = v(-Cos - Sin ) = v(-Cos - Sin ) = (-Cos - Sin )

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

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