Centripetal and Centrifugal Force and Acceleration

Centripetal and Centrifugal acceleration - force due to circular motion

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

centripetal acceleration force

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

ac = v2 / r         (1)

where

ac = centripetal acceleration (m/s2)

v = velocity (m/s)

r = circular radius (m)

Centripetal Force

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

Fc = m ac

    = m v2 / r         (2)

where

Fc = 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

Fc = (1000 kg) ((50 km/h)(1000 m/km) / (3600 s/h))2 / (200 m)

    = 965 N

Online Centripetal (Centrifugal) Calculator - Velocity

m - mass (kg)

v - velocity (m/s)

r - radius (m)

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

Fc = m v2 / r

    = m (n 2 π  r / 60)2/r

    = 0.01097 m r n2       (3)

where

n = revolution per minute - rpm

Online Centripetal (Centrifugal) Calculator - rpm

m - mass (kg)

n - rpm

r - radius (m)

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

Related Topics

  • Dynamics - Dynamics Motion - velocity and acceleration
  • Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects

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