# What is the formula for centripetal acceleration?

A. F = ma
B. E = mc²
C. ac = v/r
D. ac = v²/r

Correct Answer: D (ac = v²/r)

## Explanation:

The formula for centripetal acceleration is given by ac = v²/r, where ac represents the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path. This formula describes the acceleration experienced by an object moving in a circular path, always directed towards the center of the circle. The greater the velocity or the smaller the radius of the circle, the greater the centripetal acceleration will be.

## Understanding the Centripetal Acceleration Formula: ac = v²/r

Centripetal acceleration is the acceleration experienced by an object moving in a circular path, always directed towards the center of the circle. This type of acceleration is necessary to keep an object moving in a circular path, as the object tends to move in a straight line in the absence of a force. The formula for centripetal acceleration is given by ac = v²/r, where ac represents the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.

This formula is derived from the principles of circular motion and can be applied to a wide range of scenarios. For example, it can be used to calculate the centripetal acceleration of an object moving in a circular path on a roller coaster or the acceleration experienced by a planet orbiting a star.

It is important to note that the formula only applies to objects moving in a circular path with a constant speed. If the speed of the object changes, the acceleration experienced by the object will also change. Additionally, the formula assumes that the circular path is uniform and that there are no external forces acting on the object.

In summary, the formula for centripetal acceleration, ac = v²/r, is an important concept in physics that is used to describe the acceleration experienced by objects moving in circular paths. By understanding this formula, we can better understand the behavior of objects in circular motion and calculate important variables such as velocity and radius.

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