In uniform circular motion, can $a$_c (centripetal acceleration) change the speed of an object moving in a circle? Choose the best explanation.

• A. No, $a$_c only changes the direction of $v$ (velocity), not its magnitude, so the speed remains constant.
• B. No, $a$_c has no effect on either the speed or direction of the object.
• C. Yes, $a$_c increases the speed of the object as it moves around the circle.
• D. Yes, $a$_c decreases the speed of the object in circular motion.

Answer: (A)

Verified step by step guidance

1. Recall that centripetal acceleration \(a_c\) is always directed towards the center of the circular path, perpendicular to the instantaneous velocity \(v\) of the object.
2. Understand that acceleration changes velocity, which is a vector quantity having both magnitude (speed) and direction.
3. Since \(a_c\) is perpendicular to \(v\), it changes only the direction of the velocity vector, not its magnitude.
4. Because speed is the magnitude of velocity, and \(a_c\) does not affect this magnitude, the speed remains constant during uniform circular motion.
5. Therefore, centripetal acceleration does not increase or decrease the speed; it only continuously changes the direction of the velocity, keeping the object moving in a circle at constant speed.