Centripetal Acceleration Calculator

Centripetal acceleration is a concept in physics that describes the acceleration of an object moving in a circular path. It is always directed towards the center of the circle or the axis of rotation and is responsible for continuously changing the direction of the object’s velocity vector. The term “centripetal” is derived from the Latin words “centrum” (center) and “petere” (to seek), indicating that the acceleration is always directed inward, seeking the center of the circular motion.

To understand centripetal acceleration, let’s first define a few key terms:

1. Velocity (v): Velocity is a vector quantity that represents the rate of change of an object’s position with respect to time. It has both magnitude and direction.
2. Centripetal Force (F_c): Centripetal force is the force that keeps an object moving in a circular path. It is always pointed in the direction of the circle’s center.

Centripetal Acceleration Formula :

Centripetal Acceleration =Velocity ²  / Radius 

where :

• Velocity = magnitude of the velocity of the object,
• Radius =  radius of the circular path.

The above formula defines that centripetal acceleration is directly proportional to the square of the object’s velocity and inversely proportional to the radius of the circular path. It means that as the speed of the object increases or the radius of the circle decreases, the centripetal acceleration will also increase.

Now, let’s see into the derivation of this formula:

Velocity Vector: The velocity vector of an object moving in a circle is always tangential to the circle at any point. This velocity vector is constantly changing direction as the object moves around the circle.

Change in Velocity: Since velocity is a vector, any change in direction constitutes acceleration. The change in velocity is always directed towards the center of the circle, leading to centripetal acceleration.

Centripetal Force and Acceleration: According to Newton’s second law of motion, the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F=ma). The centripetal force and the centripetal acceleration are the net forces and accelerations in the case of circular motion.

Centripetal Force Expression: Centripetal force can be expressed : Mass . Velocity ²  / Radius

Centripetal Acceleration Formula: Substituting Fc​=ma into the centripetal force expression and rearranging, we get

Centripetal Acceleration = Velocity ²  / Radius

In summary, centripetal acceleration is the acceleration directed towards the center of a circular path and is necessary for an object to maintain circular motion. The formula : Centripetal Acceleration Velocity ²  / Radius , quantifies this acceleration, emphasizing its dependence on the square of the object’s velocity and the inverse of the radius of the circular path. Understanding centripetal acceleration is crucial in various fields, including physics, engineering, and astronomy, where circular motion is prevalent.