Centripetal and Centrifugal Force and Acceleration

Centripetal and Centrifugal acceleration and force due to circular motion

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 = v²/r (1)

where

a_c = 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

F_c = m a_c

    = m v²/r (2)

where

F_c = centripetal force (N)

m = mass (kg)

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*1000/3600 (m/s))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

F_c = m v²/r

    = 4 m π² n² r / 60 (3)

where

n = revolution per minute - rpm

Online Centripetal (Centrifugal) Calculator - rpm

m - Mass (kg)

n - rpm

r - Radius (m)

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