Centripetal acceleration

Round a corner and you are accelerating, even at a rock steady speed. The AP Physics 1 CED defines centripetal acceleration as the component of an object's acceleration directed toward the center of its circular path, with magnitude equal to the ratio of the tangential speed squared to the radius.

$a_c = v^2/r$ is what the AP Physics 1 and AP Physics 2 sheets print. The AP Physics C: Mechanics sheet prints the line extended, $a_c = v^2/r = r\omega^2$, the form to use when a problem gives an angular speed rather than a linear one.

It is an acceleration, not a force. No arrow labeled centripetal force belongs on a free body diagram: gravity, tension, friction or a normal force does the job, and Newton's second law reads $F_{\text{net}} = m a_c$ pointing inward. The CED notes that centripetal acceleration can result from a single force, more than one force, or components of forces.

When the speed is changing too, the net acceleration is the vector sum of the centripetal and tangential parts, so a car speeding up through a bend accelerates neither straight inward nor straight forward.

One derived result the CED names: at the top of a vertical circular loop, the minimum speed to maintain circular motion is $v = \sqrt{gr}$, the case where gravity alone supplies the centripetal acceleration.

Force analysis lives in the centripetal force guide.