You may have heard or read the following statements in relation to centrifugal force and centripetal force:
“Centrifugal force isn’t a real force.”
“It depends on the frame of reference.”
“They both act on the same body but in opposite directions.”
To be clear, only one of the three statements above is correct. This goes to show that there is quite a bit of confusion and misunderstanding between the two concepts. Hopefully, this article will clear up some of the air so that by the end of it, one can clearly and accurately distinguish the two.
Who discovered the centrifugal force?
The term “centrifugal force” was first used in 1659 by a Dutch physicist and mathematician, Christiaan Huygens. However, this phenomenon was not at all new at the time.
The idea of centrifugal force was hinted at by Italian scientist Galileo Galilei in his 1632 publication, “Dialogue on the Two Chief Systems of the World”. But Galileo didn’t develop the idea much further.
French philosopher and mathematician, René Descartes, also explored the concept in relation to planetary orbits with limited success. Sir Isaac Newton himself ran into the centrifugal force problem while developing his ideas about motion and gravity.
Ultimately, it fell on Christiaan Huygens to first coin the term “centrifugal force” and correctly derive its mathematical expression.
Although Christiaan Huygens is generally credited for the discovery of centrifugal force, Sir Isaac Newton seemed to have already used the mathematical expression ahead of him but hadn’t yet published his work*.
You may be interested to know that Christiaan Huygens lived around the same time as Sir Isaac Newton and their lines of work crossed a few times in their careers. They were both Fellows of the Royal Society, with Huygens being the first foreigner elected after the grant of its charter in 1663.
Origin of centripetal force and centrifugal force
Centripetal and centrifugal force arise when a body in motion follows a circular trajectory. In fact, the term “centri-” hints at something “circular” in its original Latin.
Centripetal force and circular motion
Imagine that you are swinging a ball attached to a string.
As you swing the ball, you will feel your fingers pulling on the cord. If you gently lose your grip, the string would slide between your fingers and the ball would move further away from the center. It’s like you are in a tug-of-war with the revolving ball.
Two points can be inferred from this experiment:
- A force is required to keep the ball moving in a circular motion. This is centripetal force – the force required to keep a body moving in a circle. All bodies moving in a circular motion are forced to do so and the force responsible is known as centripetal force.
- Centripetal force is radially directed toward the center of the circle. It acts along a line connecting the body in a circular motion to the center of the circle (the string in our case). It’s as if you are pulling the body towards your hand, with your hand being the center of the circle.
The direction and subsequent mathematical expression for centripetal force can be deduced from the geometry of the body in a circular motion. This article does not cover the analytical treatment or mathematical derivation of centripetal force, however, the interested reader can find the resources in this video.
Centripetal force is NOT a “specific” force
Centripetal force is a general term that describes a force required to keep a body moving in a circle. It doesn’t tell us anything specific about the nature or source of the force. It could be electrical (such as an electron moving around the nucleus) or gravitational (such as the Moon revolving around the Earth), or the tension in the string when swinging a ball around in a circle.
Simply put, it is a name given to any force that is required to keep a body moving in a circle.
In everyday language, centripetal force would be like the movie character, James Bond. Any actor can play James Bond. It is simply a generic name for anyone playing the role of James Bond in a 007 movie and does not point to anyone in particular.
Frames of References
Seat belts!
There is a reason seat belts are found in vehicles and not in, say, movie theatres.
Vehicles tend to accelerate, decelerate, round a corner, and on rare occasions, topple over and run into other things. Seat belts ensure that passengers remain strapped to their seats for both safety and convenience.
On the other hand, a movie theatre is far less likely to accelerate, decelerate, round a corner, or run into other buildings. Hence, there is no need for seat belts in a movie theatre.
Inertial Frames of References
A movie theatre corresponds to what physicists call an inertial frame of reference. The term ‘inertial’ hints at the concept of inertia – which is the tendency of a body at rest to resist motion and a body in motion to resist a change to its motion.
Simply put, in an inertial frame of reference a body at rest remains at rest and a body in motion continues in motion as long as there is no net force acting on them.
All references in which the principle of inertia holds true are known as inertial frames of reference. A movie theatre is a good example.
For instance, assume you are sitting in a movie theatre with a pack of popcorn beside you. Then you suddenly see the pack of popcorn sliding off the seat and falling to the floor all on its own.
That would violate the principle of inertia which requires a body at rest to resist motion – i.e. it couldn’t move on its own.
Non-inertial Frame of Reference
The frame in which the principle of inertia is violated is known as a non-inertial frame. An accelerating or decelerating vehicle is a good example.
In this frame, a book placed on the dashboard of an accelerating vehicle, for example, would slide off and fall to the floor even though no one has pushed it. Bodies at rest do not always remain at rest. Which is why you find seat belts in vehicles.
Centrifugal force and frames of reference
Imagine yourself observing a car that is rounding a curve to the left. From your perspective on the ground, the car is following a circular motion. Following our previous argument, you conclude that the car is experiencing centripetal acceleration and therefore constitutes a non-inertial frame of reference.
Inside the car is a little insect scuttling along the floor. It suddenly finds itself sliding across to the right. The poor insect has no knowledge of the car making a turn and so it wouldn’t understand why or what is pushing it. If the insect was flying mid-air inside the car rather than scuttling along the floor, it would find itself seemingly veering to the right and smashing into the wall.
But from your perspective on the ground, this behavior is quite natural; the little insect is simply trying to obey the principle of inertia by resisting changes to its motion. In this case, the insect continues with its original motion and it is the vehicle that is sliding to the left from under it.
However, from the insect’s perspective in the non-inertial frame of the vehicle; it must ascribe its sliding motion to some force that is pushing it to the right. There are no objects in the insect’s environment that are responsible for such a force so this force is completely imaginary or as physicists call it, a pseudo-force.
A pseudo force is a fictitious force that appears to act on a body when viewed in a non-inertial frame of reference. In an inertial frame, pseudo forces disappear and there is no need to bring them up.
In this case, the pseudo force is known as centrifugal force and it means a force directed away from the center.
Is centrifugal force a real force?
It depends on who you ask.
The little insect on the vehicle tells you that it is a very real force. Whilst any observer standing on the ground would tell you it’s not real.
Pseudo forces are very real to those that experience them.
There are also practical devices that make use of them. Consider the centrifuge, one of the most useful laboratory instruments. As a mixture of substances moves rapidly in a circle, the more massive substances experience a larger centrifugal force and move farther away from the axis of rotation. The centrifuge thus uses a pseudo force to separate substances by mass.
Why don’t the centrifugal force and centripetal force cancel each other?
A common misconception is that centripetal force is directed toward the center of the circle whilst centrifugal force is directed away from the center. This gives the impression of two, equal and opposite forces acting on a body – implying that they ought to cancel each other out somehow.
Others think that centrifugal and centripetal forces are an action and reaction pair as predicted by Newton’s third law of motion.
Both views are wrong. I will start by debunking the first one.
Centripetal and centrifugal forces are not action-reaction pairs.
In its most descriptive sense, Newton’s third law of motion states:
“When one body exerts a force on another, the second exerts a force on the first. These two forces are always equal in magnitude and opposite in direction.”
Let’s break this down.
Firstly, it involves more than one body i.e. body ‘A’ exerting a force on body ‘B’ and body ‘B’ exerting a force on body ‘A’. This does not fit the presumed centripetal-centrifugal force arrangement in which both forces are acting on the same body.
Secondly, Newton’s laws are only valid in inertial frames of reference. Centrifugal forces arise in non-inertial frames and are therefore non-Newtonian. Here is an in-depth analysis of inertial and non-inertial frames.
Centripetal force and Centrifugal force do not act on the same body
Broadly speaking, centripetal and centrifugal forces are mutually exclusive. They cannot coexist in the same frame of reference.
Centripetal forces arise when a body in circular motion is analyzed from an inertial frame of reference. From this perspective, there is no need to invoke centrifugal force because there is no need. Much like there is no need to enforce seatbelts in movie theatres.
Centrifugal force, on the other hand, arises when we analyze a body in circular motion from its non-inertial point of view. From this perspective, there is no need for a centripetal force. In fact, there’s no even telling that you are in circular motion, much like the poor insect would realize that it is moving in a rounding vehicle.
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