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Centripetal and Centrifugal Acceleration Force

Forces due to circular motion and centripetal / centrifugal acceleration.

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

Centripetal acceleration - forces due to circular motion

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 the centripetal acceleration - and can be expressed as

a c = v 2 / r

= ω 2 r

= (2 π n rps ) 2 r

= (2 π n rpm / 60) 2 r

(π n rpm / 30) 2 r (1)

where

a c = centripetal acceleration (m/s 2 , ft/s 2 )

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

r = circular radius (m, ft)

ω = angular velocity ( rad /s)

n rps = revolutions per second (rev/s, 1/s)

n rpm = revolutions per min (rev/min, 1/min)

Centripetal Force

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

F c = m a c

= m v 2 / r

= m ω 2 r

= m (2 π n s ) 2 r

= m (2 π n rpm / 60) 2 r

= m (π n rpm / 30) 2 r (2)

where

F c = centripetal force (N, lb f )

m = mass (kg, slugs )

According to Newton's Third Law the centripetal force acting on the object has a centrifugal force of the same magnitude acting in the opposite direction.

Example - the Centripetal Acceleration and Force acting on a Car through a Curve

road banked turn

Metric Units

A car with mass 1000 kg drives through a curve with radius 200 m at speed 50 km/h . The centripetal acceleration can be calculated as

a c = ((50 km/h) (1000 m/km) (1/3600 h/s)) 2 / (200 m)

= 0.965 m/s 2

= 0.1 g

where

1 g = acceleration of gravity (9.81 m/s 2 )

The centripetal force can bee calculated as

F c = (1000 kg) ( 0.965 m/s 2 )

= 965 N

= 0.97 kN

Related to the gravity force - weight :

F g = (1000 kg) (9.81 m/s 2 )

= 9810 N

= 9.8 kN

Imperial Units

A car with weight (gravity force) 3000 lb travels through a curve with radius 100 ft with speed 15 miles/h .

The mass of the car can be calculated as

m = (3000 lb) / (32 ft/s 2 )

= 94 slugs

The centripetal acceleration can be calculated as

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

= 4.84 ft/s 2

The centripetal force can bee calculated as

F c = (94 slugs) (4.84 ft/s 2 )

= 455 lb f

Centripetal (Centrifugal) Calculator - velocity

This calculator can be used if the velocity of an object is known - like a car in a turning curve.

Centripetal force acting on a car in a curve

Centripetal (Centrifugal) Force - rpm

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

F c = 0.01097 m r n rpm 2 (3)

where

n rpm = revolution per minute (rpm)

Centripetal (Centrifugal) Calculator - rpm

This calculator can be used if revolution speed of an object is known - like a turning bowl in a lathe.

Centrifugal Force

Force is an abstraction representing the push and pull interaction between objects.  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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Related Topics

  • Dynamics

    Motion - velocity and acceleration, forces and torque.
  • Mechanics

    Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

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