Centrifugal Force Equation, Definition, Principle

Centrifugal Force Equation

Centrifugal force – As a mass rotates about an axis, it exerts an outward radial force called centrifugal force on the axis or on any arm or rope coming from the axis to restrict its movement along a straight line (tangent).

In the following. equations:

F = Wv2 / gR
F = mv2 / R


F = centrifugal force in lbs or kg
m = Mass in lbs or kg
W = weight or mass of revolving body in lbs or kg
v = velocity at radius R on body in ft/sec or m/sec
g = acceleration due to gravity = 32.16 ft/ sec/sec
R = perpendicular distance in feet or meters from axis of rotation to center of mass, or for practical use, to center of gravity of revolving body

Linear speed:
Angular speed:

Centrifugal acceleration:
Centrifugal force:

Centrifugal Force Definition

Centrifugal force is the inertial force produced by every rotating object. It is only needed in a rotating frame of reference – or in other words, when we are viewing the system from the perspective of a moving object.

According to Newton’s first law, if there is no force acting on an object, it will move in a straight line. In order for rotation to occur, a centrifugal force must be applied that acts outward from the center of rotation.

For example, you can imagine a rock spinning on a rope. Centrifugal force is the force that prevents it from moving towards the center of rotation (i.e. towards your hand).

Centrifugal force Principle

  • The centrifugal force is fictitious or pseudo as it only exists when a centripetal force is present.
  • When a car with passengers turns the wheel, the vehicle is driven by the centripetal force that acts on all parts of the vehicle.
  • However, the passengers in the car retain the freedom of their movement and thus maintain a straight path when the vehicle begins to turn.
  • This causes the passengers to move towards the edge of the seat towards the door, which transmits the centripetal force to the passengers.
  • The force experienced by the passengers away from the car is the centrifugal force.
  • Newton’s law of motion doesn’t consider this a real force as according to Newton’s second law of motion, acceleration is caused by force.
  • When a stone at the end of the string tied to a pole on the ground is rotated, the direction of the velocity of the stone changes continuously, which creates acceleration.
  • If the string breaks, the stone tends to retain its inertia and move in a straight line tangent to the circular path.
  • If the centrifugal force was real, the stone would move in an outwards direction instead of moving tangentially.

Centripetal Force and Centrifugal Force

Comparison BasisCentrifugal forceCentripetal force
DefinitionCentrifugal force is an outward fictitious force that is experienced by an object moving in a circular path directed away from the center of rotation.Centripetal force is the force acting on a body moving in a circular path along the radius of the circular path and is directed towards the center of the circle.
DirectionIt is directed away from the center of the circle of rotation.It is directed towards the center of the circle of rotation.
NatureIt is considered a fictitious or pseudo force but has real effects.It is a real force and has real effects.
RoleCentrifugal force doesn’t have an independent existence.A circular motion doesn’t exist without centripetal force.
EquationF = mv²/rF = mv²/r
OriginThe origin of the centrifugal force is due to inertia.The origin of the centrifugal force is due to the interaction between two objects.
ActionCentrifugal force acts only in the rotating frame (non-inertial frames).The centripetal force acts in both inertial and non-inertial frames.

Centrifugal Force Applications

Although Newton’s law does not hold centrifugal force to be real, it has various applications:

  • Centrifuges work on the principle of centrifugal force. The centrifugal force generated by the rotor induces a hydrostatic pressure gradient in the tube perpendicular to the axis of rotation. This causes greater buoyancy to push the less dense particles inward while the denser particles move outward. This principle allows particles to be separated according to their density.
  • A centrifugal governor is a system that maintains a constant speed of an engine by radially moving fuel or working fluid caused by centrifugal force.
  • Centrifugal force is used to create artificial gravity in a rotating space station. These stations help to study the gravitational effects of other plants in a simulated manner.
  • Washers and dryers also use centrifugal force, where the rotation of the rotor in the washing machine creates centrifugal force that moves the laundry away from the center. This causes water to be squeezed out of the wet garment through the holes in the chamber.
  • Centrifugal force is used in various rides in amusement parks, where the force pushes the rider against the wall and allows the passenger to be lifted above the floor of the machine.
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