centripetal force vs centrifugal

2 min read 18-03-2025

Centripetal and centrifugal forces are often confused, even by those familiar with physics. While they are intimately related and appear to act in opposite directions, they represent fundamentally different concepts. This article will clarify the distinction, explaining each force and its role in circular motion.

What is Centripetal Force?

Centripetal force is the force that keeps an object moving in a circular path. It always acts towards the center of the circle. Without centripetal force, an object in motion would travel in a straight line, as dictated by Newton's first law of inertia. Think of swinging a ball on a string: the tension in the string provides the centripetal force pulling the ball inward.

Several forces can act as centripetal forces, depending on the situation:

Gravity: This is the centripetal force responsible for keeping planets in orbit around the sun and the moon orbiting the Earth.
Tension: As in the example of the swinging ball, tension in a rope or string can provide the centripetal force.
Friction: Friction between tires and the road provides the centripetal force that allows a car to turn a corner.
Normal force: The normal force from a banked track provides the centripetal force for a car going around a curve.

Calculating Centripetal Force

The magnitude of the centripetal force (Fc) can be calculated using the following formula:

Fc = mv²/r

Where:

m = mass of the object
v = velocity of the object
r = radius of the circular path

This equation shows that centripetal force is directly proportional to both mass and the square of velocity, and inversely proportional to the radius of the circular path. A larger mass, higher velocity, or smaller radius requires a stronger centripetal force.

What is Centrifugal Force?

Unlike centripetal force, which is a real force, centrifugal force is an inertial or fictitious force. It's not a force acting on the object, but rather an apparent outward force experienced by an observer in a rotating frame of reference.

Imagine you're on a merry-go-round. You feel a force pushing you outwards. This is the centrifugal force. However, from the perspective of someone standing still outside the merry-go-round, there's no outward force. The person on the merry-go-round is simply continuing in a straight line, while the merry-go-round is rotating underneath them. Their inertia resists the change in direction imposed by the circular motion.

Centrifugal Force in Different Frames of Reference

The key difference lies in the frame of reference:

Inertial frame (stationary observer): Only the centripetal force exists. The object is accelerating towards the center of the circle.
Non-inertial frame (rotating observer): Both centripetal and centrifugal forces appear to act. The centrifugal force appears to balance the centripetal force, resulting in no net force from the perspective of the rotating observer.