# Connecting Newton's 3rd law of motion to circular motion

• sofiasherwood
In summary, Newton's third law of motion can be applied to circular motion by understanding that there is an equal and opposite force acting on both objects involved. In the case of the Moon and Earth, the real force in the action-reaction couple is the force of gravity between the two objects. This causes both objects to orbit around their common center of mass. The term "centrifugal force" is often used to describe this effect, but it is not a real force and is simply a mathematical convenience for modeling the behavior of objects in a rotating frame of reference. In circular motion, the equal and opposite forces are both directed towards the center of mass. In the case of objects connected by a string, there is also a tangential component
sofiasherwood
I am confused about connecting Newton's third law of motion to circular motion.
For example, the Moon goes around the Earth in a circular orbit. There is a centripetal force (caused by gravity) that pulls the Moon inwards. However according to Newton's First law, the law of inertia, the Moon wants to continue moving in a straight line and its this conflict (cant think of another word) of the Moon wanting to continue its straight line and the centripetal force pulling it in which causes a circular motion. This hopefully, I have got correct. Newton's Third law states that when one object exerts a force on another object, then that object exerts an equal (but opposite in direction) force on the first object. Using this law and applying it to the Moon and Earth, there must be a force that is equal to and acting in the opposite direction as the centripetal force. I have researched this on the internet and found that people say this force is called centrifugal force. However, I have researched centrifugal force on the internet and found that it is not a actual REAL force. So going back to Newton's third law which states there should be a REAL force acting opposite to centripetal force, I am confused to what this actual REAL force is. I have spent ages and ages trying to understand this but I am so confused. Any help would be very much appreciated, as I was hoping to do my essay on explaining Newton's laws of motion and how they are connected to circular motion. Thanks

The real force in the action-reaction couple in your case with Moon&Earth is the force the Moon exerts upon the Earth.
That force is equal and opposite to the force the Earth acts upon the Moon with.

The result is that BOTH the Earth and the Moon go in elliptical orbits about their common center of mass.

Because the Earth has so much more mass than the Moon, the Earth's orbit around the C.M is tiny, while the Moon's orbit is appreciable.
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This phenomenon, of the most massive object making a tiny orbit due to the influence of a smaller object has been very important in detecting planets around faraway stars.
One of the techniques to discover the existence of such planets is to see such a wobbling of the star (which has its own telltale sign in the Doppler shift of the frequency of light emitted by the star, reaching us)

So can you say that the Moon also causes a centripetal force pulling the Earth in, but because the mass of the Moon is a lot smaller than the mass of the Earth, this effect is relatively small. So would the answer be to my original post, the opposite force to the centripetal force is the Moon itself pulling the Earth towards it?.

"So would the answer be to my original post, the opposite force to the centripetal force is the Moon itself pulling the Earth towards it?"

That is basically correct!

The force of gravity is strictly attractive, so that BOTH the Earth and the Moon seek to draw the other closer towards itself.
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Thank you very much for explaining this to me. Can I also ask, centrifugal force is not a real force then why do we even use this term? Is there a reason why we have given a name to something that doesn't even exist?

sofiasherwood said:
Thank you very much for explaining this to me. Can I also ask, centrifugal force is not a real force then why do we even use this term? Is there a reason why we have given a name to something that doesn't even exist?

Because sometimes it's very convenient to pretend that it does exist. For example, if you are trying to model the behavior of material in a rotating drum (how fast do you need to spin the centrifuge to separate the solid from the liquid?), the math will be easier if you pretend that there is a centrifugal force pushing stuff towards the outside instead of calculating the real forces from the circular accelerations.

Another example is in weather prediction: Cyclones, hurricanes, and typhoons acquire their spinning motion when the air mass wants to go in straight line while the curved surface of the Earth is rotating underneath it, but the math is much easier if we think of the air as being pushed sideways by a fictitious force (called the Coriolis force) that gets stronger as you move closer to the equator.

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Basically (within classical mechanics), "fictitious forces" occur naturally when we formulate the appropriate laws of motion within an accelerating frame of reference.

Thus, it is a mathematical convenience to term the effects due to the acceleration of the frame of reference them as "fictitious forces" acting upon objects whose motion are described within that frame of reference.

Suppose you are accelerating along the road.
In the frame of reference where YOU are considered stationary, all objects outside the car window are seen to be accelerating backwards.

Agreed?

Thus, within that frame of reference, the trees, the houses and so on all experience a fictitious force whose effect is to accelerate them backwards.

I understand it now. Thanks for all your help.

Welcome to PF, by the way!

Cheers :-)

In the case of a two objects orbiting about a common center of mass due to an attractive force like gravity, the equal and opposing forces are both towards the common center of mass. The equal and opposing force to the attractive force on one object is the attractive force on the other object. If the orbits are circular (as opposed to elliptical), then the Newon third law pair of forces are centripetal. If the orbits are elliptical, then most of the time there is also a tangental (in the direction of velocity) component of force on each object.

In the case of two objects moving in a circular path about a common center of mass because they are connected by a string under tension, then at each end of the string, the string exerts a centripetal force on the object, and the object exerts a reactive centrifugal force on the string. Note that the Newton third law pair of forces at each end act on different things: one force on the circling object, the other force on the end of the string.

Wiki articles:

http://en.wikipedia.org/wiki/Reactive_centrifugal_force

http://en.wikipedia.org/wiki/Centrifugal_force

rcgldr said:
If the orbits are circular (as opposed to elliptical), then the Newon third law pair of forces are centripetal. If the orbits are elliptical, then most of the time there is also a tangental (in the direction of velocity) component of force on each object.

Could you explain this in a example please.

rcgdlr is concerned with the STRICT definition of "centripetal" and "centrifugal" accelerations/forces, namely "centripetal" meaning "towards the local center of curvature", "centrifugal" "away from the local center of curvature".

On an elliptical orbit, besides acceleration towards the center, you also have acceleration along the path you are following.

The latter is called TANGENTIAL acceleration, and changes the SPEED of the the object, whil "centripetal" acceleration effects a change in the DIRECTION of the object's velocity (but not a change in its speed)

so basically in a circular orbit the acceleration is only directed inwards. But in a elliptical orbit, the acceleration is directed inwards and in the direction of its velocity. So is this what gives rise to a elliptical orbit and not circular orbit, because the acceleration is unbalanced or greater? I'm not sure if these are the right words to describe it.

I really apologise, that last statement doesn't make sense. I am struggling to explain it. What I am basically asking is, does the tangential acceleration cause the orbit to become elliptical and not follow a circular orbit?

"so basically in a circular orbit the acceleration is only directed inwards."

I didn't say that.

I said that you can't have an elliptical orbit unless you also have tangential acceleration.

This is, the case, for planetary orbits.
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It is, however, to have a strictly circular orbit with tangential accelerations as well, but such orbits are NOT possible only under the influence of gravity (other forces would have to be present as well).

When only gravity acts (simplifying to two objects), the only closed orbits that exists are ellipses, and the special case of that known as the circle.

sofiasherwood said:
I really apologise, that last statement doesn't make sense. I am struggling to explain it. What I am basically asking is, does the tangential acceleration cause the orbit to become elliptical and not follow a circular orbit?

Essentially, a strictly circular orbit is not a very stable state, change the governing parameters just a litte bit, and the actual orbit will be an ellipse, rather than a circle.

"It is, however, to have a strictly circular orbit with tangential accelerations as well, but such orbits are NOT possible only under the influence of gravity (other forces would have to be present as well)."

Would I be right in saying because the Moon is in space (a vacuum) only gravity is acting and therefore the Moon as a elliptical orbit. But in order for things to have a exactly circular orbit there must be other forces? Or have I misunderstood your statement?

sofiasherwood said:
"It is, however, to have a strictly circular orbit with tangential accelerations as well, but such orbits are NOT possible only under the influence of gravity (other forces would have to be present as well)."

Would I be right in saying because the Moon is in space (a vacuum) only gravity is acting and therefore the Moon as a elliptical orbit. But in order for things to have a exactly circular orbit there must be other forces?
No.
A strictly circular orbit is a VALID solution in planetary motion, but an EXTREME CASE relative to elliptical orbits. In that case, however (of planetary circular motion only under the influence of gravity), the speed of the object would be CONSTANT; in order to get strictly circular orbits with non-constant speed, you would need other forces acting as well.

Thanks, I mostly understand it now. Its the first time I have ever really thought about elliptical orbits, so its all new for me and a bit to get my head around.

sofiasherwood said:
Would I be right in saying because the Moon is in space (a vacuum) only gravity is acting and therefore the Moon as a elliptical orbit. But in order for things to have a exactly circular orbit there must be other forces?

No, you can have an absolutely perfectly circular orbit with just gravity at work.

But that will happen only if the orbiting body has exactly the right speed and it is exactly tangential - the least little deviation and the orbit will be slightly elliptical instead. Thus, although the perfect circular orbit is theoretically possible, without a magician to create the exact right initial conditions the best you'll get is an ellipse that is very very close to a perfect circle.

Nugatory said:
No, you can have an absolutely perfectly circular orbit with just gravity at work.

But that will happen only if the orbiting body has exactly the right speed and it is exactly tangential - the least little deviation and the orbit will be slightly elliptical instead. Thus, although the perfect circular orbit is theoretically possible, without a magician to create the exact right initial conditions the best you'll get is an ellipse that is very very close to a perfect circle.

Thanks for your response. I think I'm getting my head around circular motion. Yay!

## 1. How does Newton's 3rd law of motion apply to circular motion?

Newton's 3rd law of motion states that for every action, there is an equal and opposite reaction. In circular motion, this law applies to the centripetal force and the centrifugal force. The centripetal force is the force that keeps an object moving in a circular path, while the centrifugal force is the equal and opposite force that acts outward on the object.

## 2. What is the relationship between Newton's 3rd law of motion and the direction of circular motion?

The direction of circular motion is dependent on the forces acting on the object. According to Newton's 3rd law, the forces must be equal and opposite, which means that the direction of the centripetal force must be towards the center of the circle, while the centrifugal force must be outward from the center of the circle.

## 3. How does Newton's 3rd law of motion affect the speed of circular motion?

Newton's 3rd law of motion does not directly affect the speed of circular motion. However, it is the centripetal force that is responsible for keeping an object moving in a circular path, and the magnitude of this force is directly proportional to the speed of the object. Therefore, a change in the speed of the object will result in a change in the magnitude of the centripetal force.

## 4. Can Newton's 3rd law of motion explain why objects in circular motion do not fly off in a straight line?

Yes, Newton's 3rd law of motion explains why objects in circular motion do not fly off in a straight line. As mentioned before, the centripetal force and the centrifugal force are equal and opposite, and they act on the object in different directions. This balance of forces allows the object to continue moving in a circular path instead of flying off in a straight line.

## 5. How can Newton's 3rd law of motion be applied in real-life situations involving circular motion?

Newton's 3rd law of motion can be applied in various real-life situations involving circular motion, such as the motion of planets around the sun, the motion of a car around a curve, or the motion of a satellite in orbit. In each of these cases, the centripetal force and the centrifugal force are at play, and they must be equal and opposite for the object to maintain its circular path.

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