Dynamiek van cirkelbeweging

Consider a test-tube in a centrifuge, moving with a constant velocity along a circular path of radius, r.

Suppose the test-tube moves through a small angle Δθ, covering arc length, Δr, in time, Δt.

Since the direction of velocity is different at each instance, the triangles formed by the velocity vectors and the radial vectors are similar.

Considering small angles, the magnitude of Δv by v equals Δr by r. Dividing the equation by Δt and rearranging the terms, Δv by Δt equals v by r times Δr by Δt.

Now, at limit Δt tends to 0, Δv by Δt is the acceleration, and Δr by Δt is the linear velocity of the object.

Therefore, the acceleration of any object in uniform circular motion is expressed as the square of linear velocity divided by its radial distance.

The term centripetal acceleration highlights that the object is accelerated towards the center of the circular path at every instant. Multiplying the acceleration with the object's mass gives an expression for the centripetal force on the object.