# Newton's third law is frame independent?

• parshyaa
In summary, Newton's third law is frame independent because real forces are frame independent. This can be proven from the Newton second law and the Galilean transformation. However, this law only holds in inertial frames. Additionally, fictitious forces do not have a third-law partner and therefore this question does not arise.
parshyaa
how can you say(prove) that Newton's third law is frame independent. you will say that as real forces are frame independent , therefore Newton's third law is also frame independent, so tell me how real forces are frame independent?

parshyaa said:
so tell me how real forces are frame independent?
Per definition.

A.T. said:
Per definition.
Ok I agree, but can you give me a reason or explanation which made scientist or anyone to frame it as a definition. how can you say that this definition is correct.

parshyaa said:
how can you say that this definition is correct.
Definitions are neither correct nor false.

weirdoguy, Vanadium 50, saybrook1 and 1 other person
parshyaa said:
how can you say(prove) that Newton's third law is frame independent. you will say that as real forces are frame independent , therefore Newton's third law is also frame independent, so tell me how real forces are frame independent?
This can be proved from the Newton second law
$$F=m\frac{d^2x}{dt^2}.$$
The transformation from one inertial frame to another is given by the Galilean transformation
$$x'=x+vt ,$$
where ##v## is a constant velocity of the frame relative to the other frame. Since this transformation is linear in ##t##, we have
$$\frac{d^2x'}{dt^2}=\frac{d^2x}{dt^2} .$$
Therefore, ##d^2x/dt^2## is frame independent. Assuming that mass ##m## is also frame independent, from the Newton second law above it follows that the force ##F## is frame independent. Q.E.D.

parshyaa
parshyaa said:
so tell me how real forces are frame independent?
Demystifier said:
The transformation from one inertial frame to another
Real forces are frame independent even across non-inertial frames, so I assumed this is what the OP asks about. As for the main question, Newtons 3rd Law holds only in inertial frames.

A.T. said:
Real forces are frame independent even across non-inertial frames, so I assumed this is what the OP asks about. As for the main question, Newtons 3rd Law holds only in inertial frames.
Yes you are right that Newtons third law is frame dependent, because fictitious force can't be felt, its a imaginary force, then how it can have a reaction pair , thanks.

Demystifier said:
This can be proved from the Newton second law
$$F=m\frac{d^2x}{dt^2}.$$
The transformation from one inertial frame to another is given by the Galilean transformation
$$x'=x+vt ,$$
where ##v## is a constant velocity of the frame relative to the other frame. Since this transformation is linear in ##t##, we have
$$\frac{d^2x'}{dt^2}=\frac{d^2x}{dt^2} .$$
Therefore, ##d^2x/dt^2## is frame independent. Assuming that mass ##m## is also frame independent, from the Newton second law above it follows that the force ##F## is frame independent. Q.E.D.
Yoo right , we can also prove it without using galilean transformation,let S and S' be inertial frame of reference, let 'P' be a particle in S', therefore aPS' = aPS - aS'S, since S' is moving uniform to S , aS'S = 0 , therefore aPS' = aPS , as accelaration of particle is same in both frames and mass is same(here) , force will also be same.

parshyaa said:
...my question was only why gravitational force is attractive?
For the same reason time moves from past to future.

parshyaa
parshyaa said:
Yes you are right that Newtons third law is frame dependent, because fictitious force can't be felt, its a imaginary force, then how it can have a reaction pair , thanks.
Before asking how a fictitious force can have third-law partner, you must ask whether it has a third-law partner.

Since it does not have a third law partner, the first question does not arise.

parshyaa

## 1. What is Newton's third law?

Newton's third law states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

## 2. How does Newton's third law relate to frame independence?

Newton's third law is frame independent, meaning that it holds true regardless of the frame of reference or perspective from which it is observed. This means that the action and reaction forces will always be equal and opposite, regardless of the point of view or reference point.

## 3. Can you give an example of Newton's third law being frame independent?

Yes, a common example is a person standing on the ground. The person exerts a downward force on the ground due to their weight, and according to Newton's third law, the ground will exert an equal and opposite force upward on the person. This is true regardless of whether the observer is standing on the ground, on a moving train, or in outer space.

## 4. How does Newton's third law impact motion?

Newton's third law plays a crucial role in understanding and predicting motion. It explains why objects move in the way they do and how forces can cause changes in an object's velocity. The equal and opposite forces from Newton's third law can either cancel each other out, resulting in no motion, or they can cause an object to accelerate in a particular direction.

## 5. Is Newton's third law always applicable?

Newton's third law is a fundamental principle of physics and applies to all objects and interactions in the universe. However, it may not always be noticeable or easy to observe in certain situations, such as when the forces involved are very small or when other forces are acting on the objects. But, in general, Newton's third law is always applicable and helps to explain many physical phenomena.

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