*a-sub-c* = *r* times* omega*-squared

centripetal acceleration equals radius times angular-velocity-squared

A point particle that is going around in a circle has an acceleration that is directed toward the center of the circle and that has a magnitude equal to the product of the radius of the circle and the square of the magnitude of the angular velocity of an imaginary line extending from the center of the circle to the particle. Centripetal acceleration can also be expressed as:

(1) |

**Note:** The expression at the top of this page
is easily derived from equation (1) by substituting for v in equation (1).

**Note:** We generally think of the angular
velocity, omega, as characterizing an object that is spinning
(rotating) on an axis rather than a point particle that is going
around in a circle. In the case of a point particle going around
in a circle, an imaginary line extending from the axis of
rotation to the point particle is indeed rotating (in a manner
similar to the way the second hand on a clock rotates). Thus we
can use angular velocity (spin rate) to characterize the particle
going around in a circle. Typically we do call such an angular
velocity the angular velocity of the particle but it means the
same thing as the angular velocity of the imaginary line that
extends from the center of the circle to the particle.