# Centripetal and Centrifugal Force and Acceleration

## Centripetal and Centrifugal acceleration - force due to circular motion

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Centripetal Force and Centrifugal Force is the action-reaction force pair associated with circular motion.

### Centripetal Acceleration

Since the direction of motion is constantly changing for a object that moves in a circular path - the object has an acceleration - named centripetal acceleration, and can be expressed as

a_{c}= v^{2}/ r (1)

where

a_{c}= centripetal acceleration (m/s^{2})

v = velocity (m/s)

r = circular radius (m)

### Centripetal Force

According Newton's second law the centripetal force can be expressed as

F_{c}= m a_{c}

= m v^{2}/ r (2)

where

F_{c}= centripetal force (N)

m = mass (kg)

According to Newton's Third Law the centripetal force acting on the object has an opposite centrifugal force.

### Example

A car of *1000 kg* travels a curve of radius *200 m* at *50 km/h*. The centripetal force can bee calculated as

F_{c}= (1000 kg) ((50 km/h)(1000 m/km) / (3600 s/h))^{2}/ (200 m)

= 965 N

### Online Centripetal (Centrifugal) Calculator - Velocity

### Centripetal (Centrifugal) Force - rpm

Equation (2) can can be modified to express centripetal or centrifugal force as a function of revolution per minute - rpm - as

F_{c}= m v^{2}/ r

= m (n 2 π^{ }r / 60)^{2}/r

= 0.01097 m r n^{2}(3)

where

n = revolution per minute - rpm

### Online Centripetal (Centrifugal) Calculator - rpm

### Centrifugal Force

Newton's third law states that

*for every acting force there is an equal and opposite reaction force*

Therefore there must be an equal and opposite reaction force to the Centripetal Force: the **Centrifugal Force**

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