What is the expression for centripetal acceleration and its direction?

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

Answer: (A)

When an object moves in a circle, its velocity is continually changing direction, so there is acceleration toward the center of the circle. The strength of this centripetal acceleration depends on how fast you’re going and how tight the circle is, and it is given by the magnitude a_c = v^2 / r. The direction is inward, toward the center of the circular path.

If you prefer using angular speed, you can also write a_c = r ω^2, since v = r ω, and both forms describe the same inward acceleration. The other expressions don’t have the correct units or direction, so they don’t represent centripetal acceleration.