Centripetal and centrifugal forces are the forces experienced by rotating objects. The centripetal force keeps an object moving in a circle and is always pointed toward the center of that circle. For instance, the gravitational force of the sun is a centripetal force that keeps the Earth orbiting around it. Meanwhile, the centrifugal force is an apparent outward force on an object that is moving in a circle. An example of centrifugal force would be the sensation you have when riding a merry-go-round that makes you want to fly outwards.
The difference between centripetal and centrifugal forces
The main difference between centripetal and centrifugal forces is that the centripetal force is the force pointing towards the center of a circle that keeps an object moving in a circular path, while the centrifugal force is the sensation that an object feels when it moves in that circular path, with that sensation seeming to push it away from the center of a circle.
People experience centrifugal force when they round a corner in a car or when an airplane banks into a turn. It occurs in the spin cycle of a washing machine or when children ride on a merry-go-round. One day it may even provide artificial gravity for spaceships and space stations - if we can get spacecraft to spin rapidly enough, the centrifugal force can provide some semblance of the normal sensation of gravity.
But centrifugal force is often confused with its counterpart, centripetal force, because they are so closely related — essentially two sides of the same coin.
Centripetal force is the name given to any force that keeps an object moving in a circle — think of a rock tied to the end of a string, with the other end tied to something or in your hand. When the string is swirled around, the tension in that string keeps the rock from flying away in a straight line. That tension points inward, toward the center of the circle. As another example, the sun’s gravity provides the centripetal force that keeps the planets moving in their orbits.
The centripetal force always points perpendicular to the direction of an object’s motion. If you're riding in a car and the road banks and curves to the left, the normal force from the banked road will push the car to the left. If the centripetal force were to suddenly disappear, the car would continue moving in a straight line.
On the other hand, centrifugal force is an apparent force that an object feels as it moves along a curved path — and that apparent force is pointed in a direction away from the center of the path of rotation, according to Christopher S. Baird at West Texas A&M University.
Note that while centripetal force is an actual force, centrifugal force is defined as an apparent force. In other words, when twirling a mass on a string, the string exerts an inward centripetal force on the mass, while mass "appears" to exert an outward centrifugal force on the string.
"The difference between centripetal and centrifugal force has to do with different 'frames of reference,' that is, different viewpoints from which you measure something," said Andrew A. Ganse, a research physicist at the University of Washington. "Centripetal force and centrifugal force are really the exact same force, just in opposite directions because they're experienced from different frames of reference."
If you are observing a rotating system from the outside, you see an inward centripetal force acting to constrain the rotating body to a circular path. However, if you are part of the rotating system, you experience an apparent centrifugal force pushing you away from the center of the circle, even though what you are actually feeling is the inward centripetal force that is keeping you from literally going off on a tangent.
Let's return to the example of the car following a banked turn. If you're watching from the outside, you can observe the centripetal force pushing the car inward toward the center, keeping it moving in a circle. But if you're riding inside the car, you instead feel a force attempting to push you away from the center of the circle — this is the centrifugal force.
Centrifugal force and Newton's laws of motion
This apparent outward force is described by Newton's laws of motion. Newton's first law states that "a body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force."
If a massive body is moving through space in a straight line, its inertia will cause it to continue in a straight line unless an outside force causes it to speed up, slow down or change direction. In order for it to follow a circular path without changing speed, a continuous centripetal force must be applied at a right angle to its path. The radius (r) of this circle is equal to the mass (m) times the square of the velocity (v) divided by the centripetal force (F), or r = mv^2/F. The force can be calculated by simply rearranging the equation — F= mv^2/r.
Newton's third law states that "for every action, there is an equal and opposite reaction." Just as gravity causes you to exert a force on the ground, the ground appears to exert an equal and opposite force on your feet. When you are in an accelerating car, the seat exerts a forward force on you just as you appear to exert a backward force on the seat.
In the case of a rotating system, the centripetal force pulls the mass inward to follow a curved path, while the mass appears to push outward due to its inertia. In each of these cases, though, there is only one real force being applied, while the other is only an apparent force.
Examples of centripetal force
There are many applications that exploit centripetal force. One is to simulate the acceleration of a space launch for astronaut training. When a rocket is first launched, it is so laden with fuel and oxidizer that it can barely move. However, as it ascends, it burns fuel at a tremendous rate, continuously losing mass. Newton's second law states that force equals mass times acceleration, or F = ma.
In most situations, mass remains constant. With a rocket, though, its mass changes drastically, while the force — in this case the thrust of the rocket motors — remains nearly constant. This causes the acceleration toward the end of the boost phase to increase to several times that of normal gravity. NASA uses large centrifuges to prepare astronauts for this extreme acceleration. In this application, the centripetal force is provided by the back of the seat pushing inward on the astronaut.
Another example of the application of centripetal force is in laboratory centrifuges, which are used to accelerate the precipitation of particles suspended in liquid. One common use of this technology is for preparing blood samples for analysis. According to Rice University's Experimental Biosciences website, "The unique structure of blood makes it very easy to separate red blood cells from plasma and the other formed elements by differential centrifugation."
Under the normal force of gravity, thermal motion causes continuous mixing, which prevents blood cells from settling out of a whole blood sample. However, a typical laboratory centrifuge can achieve accelerations that are 600 to 2,000 times that of normal gravity. This forces the heavy red blood cells to settle at the bottom and stratifies the various components of the solution into layers according to their density.
This article was updated on Nov 11, 2021 by Live Science editor, Ben Biggs.
Additional resources
You can read more about the basics of centripetal force from the Swinburne University of Technology. SciShow provides a great video introduction to the topic where they explain and compare centripetal and centrifugal forces. And Khan Academy offers a mathematical discussion of the topic in this article.
Bibliography
Kuhn, Karl F., "Basic Physics: A Self-Teaching Guide", Jossey-Bass (2020)
Morin, David, "Introduction to Classical Mechanics", Cambridge University Press (2008)
