In uniform circular motion, centripetal acceleration is directed toward the center of the circle. Which statement is true?

In uniform circular motion, centripetal acceleration is directed toward the center of the circle. Which statement is true?

• A. It is directed toward the center of the circle
• B. It is directed outward from the center
• C. It is directed perpendicular to the radius
• D. It is independent of velocity

Answer: (A)

In uniform circular motion, the speed is constant but the direction of motion is continuously changing along the circle. Acceleration is the rate at which velocity changes, and here that change is a continual turning of direction toward the center. So the acceleration points inward, along the radius toward the circle’s center. This inward, or centripetal, acceleration has magnitude a = v^2/r, which shows it grows with speed and depends on the radius. The outward statement isn’t correct because motion stays bound to the circle by an inward force; saying it’s perpendicular to the radius would put the acceleration along the tangent (the direction of velocity), not toward the center. And the idea that acceleration is independent of velocity is false since faster speeds require a stronger inward acceleration to keep the path circular.

In uniform circular motion, the speed is constant but the direction of motion is continuously changing along the circle. Acceleration is the rate at which velocity changes, and here that change is a continual turning of direction toward the center. So the acceleration points inward, along the radius toward the circle’s center. This inward, or centripetal, acceleration has magnitude a = v^2/r, which shows it grows with speed and depends on the radius.

The outward statement isn’t correct because motion stays bound to the circle by an inward force; saying it’s perpendicular to the radius would put the acceleration along the tangent (the direction of velocity), not toward the center. And the idea that acceleration is independent of velocity is false since faster speeds require a stronger inward acceleration to keep the path circular.