# 605 Centripetal Force

If an angle of 90° is maintained between the (net) force and the velocity of an object, only the direction of the velocity changes. The speed does not. The resulting motion is uniform circular motion.

The magnitude of the required centripetal force is related to the speed and radius of circular motion by the formula $m\frac{{{v}^{2}}}{r}$.

For the same v, a stronger centripetal force F would result in a tighter circular motion. In the animation below, the objects are experiencing centripetal forces of 4F, 2F and F, resulting in circular motion of radii R, 2R and 4R.

For the same F, a lower speed v would result in a tighter circular motion. In the animation below, the objects have speeds of 1/√2 v, v and √2v, resulting in circular motion of radii R, 2R and 4R.