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

Velocity is a vector - specifying how fast (or slow) a distance is covered and the direction of the movement. Since the velocity vector (the direction) of a body changes when moved in a circle - there is an acceleration.

This  acceleration is named centripetal acceleration and can be expressed as

ac = v2 / r         (1)

where

ac = centripetal acceleration (m/s2, ft/s2)

v = velocity (m/s, ft/s)

r = circular radius (m, ft)

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, lbf)

m = mass (kg, slugs)

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

Example - Centripetal Acceleration acting on a Car through a Curve

Metric Units

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

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

   = 0.965 m/s2

The centripetal force can bee calculated as

Fc = (1000 kg) (0.965 m/s2)

    = 965 N

Imperial Units

A car of 3000 lb travels a curve of radius 100 ft at 15 miles/h.

The mass of the car can be calculated as

m = (3000 lb) / (32 ft/s2)

   = 94 slugs

The centripetal acceleration can be calculated as

ac = ((15 miles/h)(5280 ft/mile) / (3600 s/h))2 / (100 ft)

   = 0.22 ft/s2

The centripetal force can bee calculated as

Fc = (94 slugs) (0.22 ft/s2)

    = 20.7 lbf

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

Related Documents

Key Words

  • en: centripetal acceleration
  • es: aceleración centrípeta
  • de: Zentripetalbeschleunigung

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