# Centrifugal Force – Definition, Formula, Examples

In the realm of physics, forces play a pivotal role in explaining the interactions and motions of objects. One intriguing and often misunderstood concept is centrifugal force.

• Centrifugal force is the apparent force that acts away from the center of a circular path.
• The force is always perpendicular to the direction of movement.
• The formula for centrifugal force is the same as for centripetal force: Fc = mv2/r. However, centrifugal force acts in an equal and opposite direction.
• The force pushes or pulls an object away from the center of rotation. For example, you feel drawn toward the side of a turning car.

### What Is Centrifugal Force?

Centrifugal force is the outward perceived force that seems to push a body away from the center of rotation when it is in a circular motion. This force is not a real force in the traditional sense. Rather, it is a result of inertia — the tendency of an object to resist any change in its state of motion.

The Formula for Calculating Centrifugal Force

The formula for centrifugal force (Fc) is:

Fc​ = mω2r = mv2/r

where:

• m is the mass of the rotating object
• r is the radius of the circular path
• ω is the angular velocity of the object
• v is the velocity of the object

### A Virtual or Pseudo Force

What sets centrifugal force apart is that it is considered a “virtual” or “fictitious” force. It does not arise from any physical interaction like gravitational or electromagnetic forces. Instead, it is an apparent force that is perceived in a rotating reference frame. In a non-rotating, inertial frame of reference, centrifugal force does not exist.

The Coriolis force is another example of a virtual force that appears in a rotating reference frame. Here, the Earth’s rotation causes the deflection of moving objects to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

### How Centrifugal Force Works

Imagine being in a car that is turning rapidly. You feel as if you’re being pushed to the side of the car opposite the turn. This sensation is the result of centrifugal force. From your perspective inside the car, it feels like a force is pushing you outward. However, in reality, it’s your body’s inertia that’s causing you to continue moving in a straight line while the car turns around you.

### Examples of Centrifugal Force

Other examples of centrifugal force are:

• A bucket of water swung in a vertical circle: The water does not spill when the bucket is upside down because the centrifugal force pushes the water towards the bottom of the bucket.
• Clothes in a spinning washing machine: The clothes are pushed to the edge of the drum, demonstrating centrifugal force.

### History

Christiaan Huygens coined the term “centrifugal force” in 1659 in De Vi Centrifuga. Centrum is Latin for “center,” while -fugus comes from the word for “fleeing or avoiding.” So, centrifugus translates as “fleeing from the center.”

Sir Isaac Newton expanded upon Huygens work in his 1678 Principia and also describe centripetal force.

### Practical Applications of Centrifugal Force

Even though it’s not a “real” force, centrifugal force has real-world application:

• Centrifuges in Laboratories: Separate substances of different densities.
• Amusement Park Rides: Rides like the “Rotor” use centrifugal force to pin riders against the wall.
• Geosynchronous Orbit: Centrifugal force counteracts the downward pull of gravity, keeping satellites in orbit. In fact, the usual way of expressing centrifugal force is as a multiple of gravity, g.
• Vehicle Dynamics: Helps in understanding and improving the stability of vehicles in turns.

### Centripetal vs Centrifugal Force

Both centripetal and centrifugal force involve rotation or circular motion, yet they are distinct in their origins and nature.

• Mutual Existence in Circular Motion: Both forces occur in scenarios where an object is moving in a circular path. While centripetal force is necessary for this motion, centrifugal force is an apparent force experienced in a rotating frame.
• Opposing Directions: Centripetal force always points towards the center of the circular path, acting as the “center-seeking” force. In contrast, centrifugal force appears to act outward from the center, providing a sensation of being “flung” outward.

#### Difference

• Nature of Forces:
• Centripetal Force: This is a real force, resulting from tangible interactions like gravitational pull, tension, friction, or any other force that causes an object to follow a curved path.
• Centrifugal Force: It’s a fictitious or pseudo force. It doesn’t arise from a physical interaction, but is rather a result of inertia in a rotating reference frame.
• Frame of Reference:
• Centripetal Force: It occurs in both inertial (non-accelerating and non-rotating) and non-inertial (accelerating or rotating) frames of reference.
• Centrifugal Force: It only appears in non-inertial, specifically rotating, frames of reference. In an inertial frame, centrifugal force does not exist.
• Purpose in Equations of Motion:
• Centripetal Force: In the physics of circular motion, centripetal force is what causes the object to deviate from straight-line motion, pulling it towards the center of the circle.
• Centrifugal Force: In a rotating frame, it explains why an object appears to move outward or why there is a need for a centripetal force to counteract this outward motion.

### References

• Hand, Louis N.; Finch, Janet D. (1998). Analytical Mechanics. Cambridge University Press. ISBN 978-0-521-57572-0.
• Kobayashi, Yukio (2008). “Remarks on viewing situation in a rotating frame”. European Journal of Physics. 29 (3): 599–606. doi:10.1088/0143-0807/29/3/019
• Restuccia, S.; Toroš, M.; Gibson, G. M.; Ulbricht, H.; Faccio, D.; Padgett, M. J. (2019). “Photon Bunching in a Rotating Reference Frame”. Physical Review Letters. 123 (11): 110401. doi:10.1103/physrevlett.123.110401
• Yoder, Joella (2013). A Catalogue of the Manuscripts of Christiaan Huygens Including a Concordance With his Oeuvres Complètes. BRILL. ISBN 9789004235656.