State the formula for centripetal acceleration and the direction of the net force for uniform circular motion.

• A. a_c = v^2 / r toward the center; F_net = m v^2 / r toward the center.
• B. a_c = v^2 / r toward the center; F_net = m v^2 / r away from the center.
• C. a_c = v^2 / r away from the center; F_net = m v^2 / r toward the center.
• D. a_c = v / r toward the center; F_net = m v^2 / r toward the center.

Answer: (A)

Centripetal acceleration points toward the center of the circular path. For uniform circular motion, the speed is constant, but the velocity is continually changing direction, so there is an inward acceleration. The magnitude is a_c = v^2 / r, with v the speed and r the radius. By Newton’s second law, the net force equals mass times acceleration, so the net force also points inward with magnitude F_net = m v^2 / r. This inward force is what continually redirects the motion toward the center; without it, the object would move in a straight line. The other ideas—an outward acceleration, or a magnitude like v/r—either contradict the necessary inward direction or have the wrong units and dependence on velocity.