A car moves at constant speed v around a flat curve of radius r. What is its centripetal acceleration a_c, and in what direction does it point?

A car moves at constant speed v around a flat curve of radius r. What is its centripetal acceleration a_c, and in what direction does it point?

• A. a_c = v^2 / r directed away from the center
• B. a_c = g sin θ directed downward
• C. a_c = v^2 / r directed toward the center
• D. a_c = v^2 / r directed horizontally toward the center

Answer: (C)

In uniform circular motion, the velocity keeps changing direction even though its speed is constant. This change in direction requires a net inward acceleration toward the center of the circle, called centripetal acceleration. Its magnitude is a_c = v^2 / r, arising from the geometry of circular motion (you can relate it to v = rω and a = v^2/r). Since the motion is on a flat surface, this inward acceleration lies in that plane and points toward the center of the curve.

In uniform circular motion, the velocity keeps changing direction even though its speed is constant. This change in direction requires a net inward acceleration toward the center of the circle, called centripetal acceleration. Its magnitude is a_c = v^2 / r, arising from the geometry of circular motion (you can relate it to v = rω and a = v^2/r). Since the motion is on a flat surface, this inward acceleration lies in that plane and points toward the center of the curve.