Centripetal Acceleration Formula

The force in the circular motion or curvilinear motion experienced by an object is directed toward the center of curvature of the path. Velocity of the object could be constant and changing over the course of the motion. Tangential velocity's direction always changes over the course of the motion. Since the quantity velocity is a vector, changing its direction will change the velocity. Since the centripetal force that makes this object to move in a perfect circular path has an inward direction of force action, the centripetal acceleration is always in a radial direction of the circular path. Centripetal acceleration is defined as the rate of change of the tangential velocity.

Definition

Centripetal acceleration is defined as the acceleration in a direction toward the center of a circular path along which the object is moving. The acceleration keeps changing the direction of an object such that it continues moving in a circular path.

Formula of Centripetal Acceleration

As discussed earlier, the centripetal acceleration is defined as the rate of change of tangential velocity, we can write it as,

Centripetal Acceleration = rate of change of tangential velocity

 We can also write it as,

 The centripetal force acting on an object moving on a circular or curvilinear path is given as,

 So, the acceleration acting on the object can be given as,

And we also know that tangential acceleration is represented by,

 

Where,

•  r is radius of curvature,

•  α is angular acceleration and

•  ω is angular speed.

Total acceleration for circular path is,

Solved Problems

Problem 1: A jet is passing through a track whose radius is 4 km. The jet is moving at a constant velocity and at a speed of 10 km/s. What is the centripetal acceleration?

Solution:

Radius of the circular track = 4 km = 4 × 1000 m = 4000 m

Velocity = 10 km/sec = 10 × 1000 m/sec = 10,000 m/sec

Hence, centripetal acceleration

Example 2: Ball has a mass of 0.2kg. It travels a circular path with the radius (r) 80 cm. Determine the centripetal force if it covers 1 round in 3 seconds.

Solution:

Mass of the ball = 0.2 kg

Radius of the path = 80 cm = 0.8 m,

Path velocity

Now we'll calculate the centripetal acceleration by this formula:

Centripetal Force is expressed as:

 

                = 0.7008 kgm/s2

 

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