Centripetal and Centrifugal Force - Acceleration

Centripetal and centrifugal acceleration - forces due to circular motion

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

ac = v2 / r  

    = ω2

    = (2 π nrps)2 r   

    = (2 π nrpm / 60)2 r   

    =  (π nrpm / 30)2 r                      (1)


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

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

r = circular radius (m, ft)

ω = angular velocity (rad/s)

nrps = revolutions per second (rev/s, 1/s)

nrpm = revolutions per min (rev/min, 1/min)

Centripetal Force

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

Fc = m ac

    = m v2 / r  

    = m ω2 r        

    = m (2 π ns)2

    = m (2 π nrpm / 60)2

    =  m (π nrpm / 30)2 r                             (2)


Fc = centripetal force (N, lbf)

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 - Centripetal Acceleration acting on a Car through a Curve

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

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

   = 0.965 m/s2

The centripetal force can bee calculated as

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

    = 965 N

    = 0.97 kN

Related to the gravity force - weight:

Fg = (1000 kg) (9.81 m/s2)

    = 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/s2)

   = 94 slugs

The centripetal acceleration can be calculated as

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

   = 4.84 ft/s2

The centripetal force can bee calculated as

Fc = (94 slugs) (4.84 ft/s2)

    = 455 lbf

Online Centripetal (Centrifugal) Calculator - velocity

m - mass of object (kg)

v - velocity of object (m/s)

r - radius of curve (m)

Centripetal (Centrifugal) Force - rpm

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

Fc = 0.01097 m r nrpm2                              (3)


nrpm = revolution per minute (rpm)

Online Centripetal (Centrifugal) Calculator - rpm

m - mass (kg)

nrpm - revolutions per minute (rpm)

r - radius (m)

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.

Related Topics

  • Dynamics - Motion - velocity and acceleration, forces and torques
  • Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more

Related Documents

Tag Search

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

Search the Engineering ToolBox

- "the most efficient way to navigate!"

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!