What is the centripetal acceleration for a body moving at 20 m/s in a circular path with a radius of 50 m?

• A. 4 m/s^2
• B. 8 m/s^2
• C. 12 m/s^2
• D. 16 m/s^2

Answer: (B)

In circular motion, the centripetal acceleration toward the center has magnitude a_c = v^2 / r. Here, the speed is 20 m/s and the radius is 50 m, so a_c = 20^2 / 50 = 400 / 50 = 8 m/s^2. The acceleration is directed toward the center of the circle. If the radius were larger, the acceleration would be smaller; if the speed increased, the acceleration would increase (since it depends on the square of speed).