# Newton's third law in non-inertial frames

• Debdutta
In summary: So in summary, Newton's third law is still valid in non-inertial frames as long as the second law is assumed to be valid and any non-inertial effects are accounted for with pseudo forces.
Debdutta
Is Newton's third law valid in non-inertial frames? For example, in a rotating frame of reference, can Newton's third law still be applied? Or does the non-inertial character of the frame violate it?

Debdutta said:
Is Newton's third law valid in non-inertial frames?

Only if the second law is not valid. But usually the second law is assumed to be valid in non-inertial frames. This results in pseudo forces violating the third law.

Welcome to PF!

Hi Debdutta! Welcome to PF!
Debdutta said:
Is Newton's third law valid in non-inertial frames?

As between two objects in contact?

Yes, the forces will still be equal and opposite.

gracy
The forces acting between two objects do not depend on the coordinate system or referemce frame you use to measure them. So the third law always holds.

The second law is different: the apparent accelerations that you measure DO depend on the reference frame, hence the second law does not hold in a accelerating frame unless you add another term to the equation (a.k.a a fictitious force) to compensate for the acceleration of the frame.

rohit dutta and gracy
So my next question is, can we assume that Newton's Third Law is still valid for interacting objects in any frame to test whether it is actually an inertial frame or not, that is, the first two laws of Newton hold or not?

Debdutta said:
So my next question is, can we assume that Newton's Third Law is still valid for interacting objects in any frame to test whether it is actually an inertial frame or not, that is, the first two laws of Newton hold or not?
Yes. You can always assume that the interaction forces between objects obey Newton's Third Law. If the sum of all interaction forces on an object and its coordinate acceleration are not consistent with Newtons Second Law, then you know that your frame is not inertial.

rohit dutta and gracy

## 1. What is Newton's third law in non-inertial frames?

Newton's third law states that for every action, there is an equal and opposite reaction. In non-inertial frames, this means that when a force is applied to an object, the object will experience an equal and opposite force in the opposite direction.

## 2. How does Newton's third law apply to non-inertial frames?

In non-inertial frames, the third law still holds true, but the forces may not cancel out completely due to the frame's acceleration. This is known as fictitious forces, which arise due to the frame's non-inertial nature.

## 3. Can Newton's third law be violated in non-inertial frames?

No, Newton's third law is a fundamental law of physics and cannot be violated in any situation, including non-inertial frames. The reaction force may not always be observable due to the frame's acceleration, but it still exists.

## 4. How does Newton's third law affect objects in non-inertial frames?

Newton's third law affects objects in non-inertial frames by causing them to experience a net force due to the acceleration of the frame. This can result in objects moving in curved paths or experiencing apparent forces, such as centrifugal and Coriolis forces.

## 5. Is it necessary to consider Newton's third law in non-inertial frames?

Yes, it is necessary to consider Newton's third law in non-inertial frames as it is a fundamental principle of physics. Ignoring this law can lead to incorrect predictions and understanding of the motion of objects in non-inertial frames.

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