What is the expression for the centripetal acceleration a_c of an object moving with speed v on a circle of radius r, directed toward the center?

• A. a_c = v^2 r
• B. a_c = v^2 / r toward the center
• C. a_c = v / r
• D. a_c = r / v^2

Answer: (B)

When an object moves in a circle at constant speed, its velocity is always changing direction, so the acceleration must point toward the center of the circle—this is centripetal acceleration. The magnitude of that inward acceleration is a_c = v^2 / r, and it can also be written as a_c = ω^2 r since v = ω r. This shows the inward acceleration grows with the square of the speed and decreases with larger radius: doubling the speed increases a_c by a factor of four, while doubling the radius halves a_c. The direction is explicitly toward the center, which is why this form correctly describes the centripetal acceleration. Other expressions don’t have the correct units or the correct dependence on speed and radius.