# If an object moving in a circle experiences centripetal force, then doesn't it also experience centrifugal force, because of Newton's third law?

When an object moves in a circle, there's an acceleration towards the center of the circle, the centripetal acceleration, which also gives us the centrifugal force (since $$F = ma$$ is the equation for a force and the acceleration of an object, therefore, is caused by a force). But according to newton's third law, for every action, there is an equal and opposite reaction, which would mean that because of the centripetal force there's an equal force outwards, which I would say is the centrifugal force. But this is obviously not true since that would mean that the net acceleration on the object moving in the circle would be 0. So my question is, what is actually this reaction force that's created by the centripetal force, and where does the centrifugal force come from? I do know that the centrifugal force can be viewed as an inertial force in a certian reference frame, but is there any way to describe it in another way? I can imagine that the centripetal force may come from friction with the road if you're in a car and if the reaction force is the force into the ground it makes sense, except for the centrifugal force.

• For every question on S.E., there an equal and opposite answer. – Andrew Sep 19 '19 at 18:02
• the centripetal and centrifugal forces being the action and reaction forces is pretty much how our physics teacher taught us – Michael Sep 20 '19 at 1:30
• Your teacher is very wrong, @Michael. There is no "equal but opposite" reaction to the centrifugal force. It, along with the Coriolis effect, are fictional forces. There is no third law reaction to fictional forces, and real forces do not have a fictional force as a third law reaction to them. – David Hammen Sep 22 '19 at 13:34

This is a common misinterpretation of Newton's third law, often stated as "to every action, there's an equal and opposite reaction." As you surmise, "action" and "reaction" refer to forces. However, they refer to forces acting on different things. Otherwise, nothing could accelerate, ever: if every force were always canceled out by an equal and opposite force, no force could ever do anything. Instead, forces occur between objects--say car and road, to take your example. The road exerts an inward force on the car, which, you're right, is the centripetal force. The equal and opposite force is exerted by the car, on the road. The two forces are acting on different things, so they do not cancel. This second force (the force exerted by the car on the road) is sometimes referred to as the "reactive centrifugal force," which is confusing, because it's different from the more common meaning of centrifugal force.

Lets look at the Earth-moon system for an example. The centripetal force is Earth's gravity, keeping the Moon from flying away. But this works both ways, the Earth is pulled towards the Moon just as hard as the moon is pulled towards the Earth.

In your car example, the angle of the front tires means some percentage of the force of the car is spent on turning the car. The opposite force is spent trying to push the roadway in the opposite direction. It's the same as driving forwards really, except your force vector isn't parallel with your velocity vector.

Quick little aside: Newton's laws, the ones you learn in High-school anyways, only work in inertial reference frames. Centrifugal force does exist in a rotating reference frame.

• oh, so what would you use instead of Newton's laws in a non-inertial frame of reference? – Melvin Sep 18 '19 at 17:45
• Still Newton's laws, just more than you learn in an average highschool physics class. – Ryan_L Sep 18 '19 at 17:46
• ok, but an inertia frame of reference is that the frame of reference or coordinate system is not moving, right? – Melvin Sep 18 '19 at 17:47
• A rotating reference frame is NOT inertial because it is accelerating. – Ryan_L Sep 18 '19 at 18:00
• In an inertial reference frame, an object is "pulled" away from the center of rotation by it's tangential inertia. In a rotating reference frame, the object has no inertia and is being pulled away by centrifugal force. Centripetal force exists in both reference frames. Whether centrifugal force or inertia is responsible depends on where the observer is. – Ryan_L Sep 18 '19 at 18:19

Imagine an object connected by a string moving in a circular motion.

what is actually this reaction force that's created by the centripetal force?

The force on a object, which causes the centripetal acceleration of an object, is due to another entity - the action, eg the force on the object due to the string.

The Newton third law pair is the force on another entity due to the object - the reaction, eg the force on the string due to the object.

where does the centrifugal force come from?

The centrifugal force is not a real force, rather it is introduced for the convenience of being able to use Newton’s second law in the rotational (non-inertial) frame of the object.

There is no Newton third law pair to the centrifugal force.

But this is obviously not true since that would mean that the net acceleration on the object moving in the circle would be 0.

That is not correct. An object is undergoing acceleration if either its speed changes, it changes direction, or both. According to Newtons first law, a body moving in a straight line at constant speed will continue to do so unless acted upon by a net external force. At any instant in time the velocity vector of a body undergoing circular motion is tangent to the circle. The inertia of the body resists a change in direction of that vector. The centrifugal force is a fictitious force that appears to be acting on the body in a non-inertial (accelerating) reference frame due to the inertia of the body. The centripetal force is the net force acting on the object forcing it to constantly change direction towards the center of the circular path.

Perhaps it is easiest to see this if you consider a car driving in a straight line at constant speed. An object is on the passenger seat. The driver (in this case on the left side of the car) makes a sharp left turn, which is the beginning of circular motion. The object on the seat slides towards the passenger side door. The driver experiences the sensation of being pushed towards the passenger side. But neither the driver nor the object is subjected to any contact force pushing them in that direction. They are experiencing a centrifugal (fictitious) force.

Now suppose instead that the object does not slide on the seat because of the static friction between the object and the seat. The static friction force is a centripetal force towards the center of the circular preventing the object from continuing in a straight line as viewed from an inertial reference frame (e.g., the road). This is the same thing that is happening in your example.

Bottom line: The centripetal force keeps changing the direction of the object towards the center of the circular path. A change in direction of the motion of an object results in an acceleration even if the speed of the object is unchanged.

Hope this helps.

• I think you may have missed the point of that comment. The OP seems to have recognized the contradiction between his intuitive notion (that centrifugal force should also apply) and the need for the object to be accelrating (and this subject to non-zero net force). Presumably that is what prompted the question. – dmckee --- ex-moderator kitten Sep 19 '19 at 15:27

which also gives us the centrifugal force (since $$F=ma$$ is the equation for a force and the acceleration of an object, therefore, is caused by a force).

You shouldn't call it "centrifugal force", but rather centripetal force. A centripetal force inwards causes the centripetal acceleration inwards. When people say "centrifugal force", they usually mean the feeling of being swung outwards, so this imaginary "centrifugal force" would be opposite to the actual centripetal force.

Note, though, that there is no such thing as a centrifugal force (it just feels like there is, but that's just an illusion); there is only a centripetal force. (I am here assuming an inertial frame of reference, such as the ground).

But according to newton's third law, for every action, there is an equal and opposite reaction, which would mean that because of the centripetal force there's an equal force outwards, which I would say is the centrifugal force. But this is obviously not true since that would mean that the net acceleration on the object moving in the circle would be 0.

A very important note: The action/reaction forces in Newton's 3rd law do not act on the same object. Your object is pulled inwards and another object is simultaneously pulled outwards (the opposite way) with an equal force.

A circular motion happens because

• you swing something around in a string (the outwards force acts on your hand)
• you turn with your car (the outwards force acts on the ground/asphault/planet)
• a satellite is orbiting Earth (the outwards force acts on the Earth)
• etc.

There is always a source of the inwards force; there is always an interaction with something else, before a force can be present. That "something else", is what feels the reaction force via Newton's 3rd law.

I can imagine that the centripetal force may come from friction with the road if you're in a car and if the reaction force is the force into the ground it makes sense, except for the centrifugal force.

You are basically answering the question here yourself. The only last thing to point out is, as mentioned above, that there is no such thing as a "centrifugal force". That is a bad term, because it is not a force. It is a feeling. You are swung outwards against the window when a car turns, not because some "centrifugal force" pushes you outwards, but because the car is pulled inwards by the centripetal force.

It is not you being pushed outwards, it is the car moving away from the straight path your body has and thus pulling you along. But from the perspective of the car it looks like you are the one moving and not the car - that is just an illusion, a trick by our brains. The same trick happens when a guy on roller skates is standing in a bus. When the bus accelerates, it looks like he rolls backwards - but it is not him rolling backwards, it is the bus rolling forwards away from underneath his feet.

In summary: It is not you moving outwards, it is the car moving into you. Nothing pushes you outwards, and there is no motion/acceleration outwards which would be caused by any force. Only the feeling/illusion of it.

• -1: This is wrong. Nothing forbids one to describe the system from a non inertial reference frame, e.g. a rotating one. In such a frame of reference, the centrifugal force is real and does exist. It isn't merely a "trick to your brain". Relevant xkcd: xkcd.com/123. – AccidentalBismuthTransform Sep 19 '19 at 9:06
• @thermomagneticcondensedboson In any frame, the pseudo-forces are nonexisting and just an illusions, a "sensation". I am throughout this answer assuming the inertial ground frame of reference. I will add that as an initial remake. Also, taking into the account the level, it is IMO a better pedagogical method to consider only intertidal frames and thus consider centrifugal forces as nonexisting. – Steeven Sep 19 '19 at 9:36

First, lets get the mistake in your first sentence out of the way. Due to $$F=ma$$, you get a centripetal force due to the centripetal acceleration.

With that out of the way, lets get to the crux of the question. You have learnt Newton's third law, "For every action, there is an equal but opposite reaction". This statement is a bit incomplete, because it does not include any information about the location of this action and reaction.

Newton's third law can be paraphrased as, "For every action of body A on body B, there exists an equal but opposite reaction of body B on body A". We have determined that body A moves in a circle, so it has some centripetal action exerted upon it. Somewhere, there must exist an equal but opposite reaction on some body B (not A!).

Typical examples of body B would be

• Your hand holding the bucket that you're swinging in a circle. You can feel this centrifugal force trying to 'pull' your hand away from your body.
• The road, being pushed 'outwards' due to the car driving in a circle
• The Earth, continuously accelerating towards the Moon (which means that the Earth is also, in a way, rotating around the Moon - in fact, they both rotate around a common barycenter)

So, centrifugal force is a nonsense word like street slang then. My high school physics teacher always told us, "It's centripetal. Don't call it centrifugal"

• ... no. Centrifugal force isn't a nonsense word. It has a sensible meaning, though "inertial forces" often confuse people. Centripetal force is something different, and would be used for different reasons. You call centripetal forces centripetal forces, and centrifugal forces centrifugal forces, so that quote from your teacher is misleading here. – JMac Sep 19 '19 at 19:42