Consider an object travelling with uniform circular motion at speed v moving in a short time-interval δt along the perimeter of a circle radius r.Let the distance moved by the object in that time be δs.If the distance is small, then δs can be considered to be a straight line.
By similar triangles δv/v = δs/rSince v = δs/δt then δs can be replaced by vδt. Rearranging gives
By similar triangles δv/v = δs/rSince v = δs/δt then δs can be replaced by vδt. Rearranging gives
| a | = | v2 r |