Centripetal Acceleration

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Acceleration of a body can be defined as the rate of change of velocity with the time taken. The equation for centripetal acceleration is:

a = dv/dt

Where "a" is the acceleration, "v" is the velocity of body and "t" is the time taken.If a body is moving along a straight line with non-uniform velocity, we call the acceleration as linear acceleration or simply acceleration. If a body moves in a circular path then the acceleration experienced by it is centripetal acceleration. We call it as centripetal acceleration because it is always directed towards the center of the circular path. SI unit of centripetal acceleration is m/s2.

The velocity vector is always tangential to the radius of the circular path as shown below. 

Let us assume the tangential acceleration is not directed along the center and is parallel to the velocity
vector or direction of motion. Considering this acceleration along the direction of motion of the horse will
change the velocity, along the path. But as the horse is running with constant velocity this contradicts our
assumption. Hence, in a uniform circular motion (constant velocity), the acceleration vector will be directed

only towards the center of the circle. This is known as centripetal acceleration as shown below. 

ac is the centripetal acceleration.

Example: For the given diagram of a stone tied at one end of the string predict the direction of velocity. 

Answer: The path traced by the stone is circular in nature. For circular motion the direction of velocity is

tangential to the radius of the path.

Example: Can an object accelerate if it is moving with uniform speed?

Answer: Yes. The object can accelerate even if it is moving with uniform speed. An object can accelerate by

three ways as follows.

1)    If the velocity is non-uniform and direction of motion is same.

2)    If the velocity is uniform but the direction is changing.

3)    If both velocity and direction are changing.

Here we have to deal with uniform velocity but changing direction. This is the case of uniform circular motion.

Velocity of the particle moving around the path is constant but the direction is changing all the time

(tangential to the radius). 

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