Question

Explain the concept of centripetal acceleration for a particle moving in a circular path at a constant speed. Describe how centripetal acceleration relates to the particle's change in direction and its velocity. Provide a step-by-step explanation of how to calculate centripetal acceleration and clarify any misconceptions about the relationship between speed, circular path length, and the time taken for the particle's velocity to return to its original vector.

Answer 1

Centripetal acceleration is the acceleration experienced by an object moving in a circular path at a constant speed. It is always directed towards the center of the circular path.

Step-by-step explanation:

In uniform circular motion, an object moves in a circular path at a constant speed. However, since the direction of the object's velocity is constantly changing, it is always undergoing acceleration. This acceleration, called centripetal acceleration, points towards the center of the circular path and is responsible for keeping the object in its circular motion.

To calculate centripetal acceleration, you can use the formula ac = v^2 / r, where ac is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.

It's important to note that centripetal acceleration is related to the change in direction of the object's velocity rather than its change in speed. Even if the object's speed remains constant, the centripetal acceleration is still present as long as it is moving in a circular path.