Is Newton's 3rd law valid in non-inertial frames?
If so, then are there other cases for which Newton's 3rd law is not applicable?
[Physics] When does not Newton’s 3rd law apply
classical-mechanicsforcesnewtonian-mechanicsreference frames
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Newton's second law says $F = ma$. Now if we put $F = 0$ we get $a = 0$ which is Newton's first law. So why do we need Newton's first law?
I don't think this is obvious from Newton's statement of the Second Law. In his Principia Mathematica, Newton says that a force causes an acceleration. Without the first law, this doesn't necessarily imply that zero force means zero acceleration. One could conceive of other things that also cause acceleration.
A modern person might be concerned about non-inertial reference frames. Someone from Newton's time would probably be more concerned about Aristotelian ideas of objects seeking their own level. But in either case, its necessary to emphasize that forces not only cause acceleration, but that they are the only things that do so (or in the modern formulation, that there exists a frame in which they are the only things that do so).
So, the total force experienced by the Earth and the object by each other is approx. 19.6 N.
I guess you are free to consider that a sum of the magnitudes of the two different forces, but it is unclear to me how that would help you. The forces still act on different bodies. The earth has a force of 9.8N on it, and the object has a force of 9.8N.
We observe that an object of 1 kg accelerates at only 9.8 m/s^2 near Earth's surface and not at 19.6 m/s^2; this means that the force experienced by a 1 kg object is 9.8 N near Earth's surface.
Yes. In fact that's exactly how you began the scenario. We can compute the force on one object and find that to be the magnitude.
You don't get to add up the magnitudes of two forces on two different objects in two different directions and think that magnitude applies to one object in one direction.
Let's assume that Newton's 3rd law of motion isn't acting for now.
That's a tough ask. We're used to forces arising from a coupled interaction. Both sides of the couple experience this interaction as a force.
So, the object and Earth each are experiencing a force of 9.8 N from each other.
That's exactly what we'd expect normally. How does this create a situation where Newton's law "isn't acting"?
Newton's 3rd law doesn't describe some additional force that pops into existence. It just says that if something creates a force (like gravity between two objects), that force is created on both (in opposite directions). That it's not possible to create a "one-way" force.
The gravitational force of 9.8N on both objects is consistent with the 3rd law.
Best Answer
There are
fictitious forceswhen you define a non-inertial frame. For more information, see these Newtonian Dynamics notes by Richard Fitzpatrick. There are two core parts of the answer:One corollary of Newton's third law is that an object cannot exert a force on itself. Another corollary is that all forces in the Universe have corresponding reactions. The only exceptions to this rule are the fictitious forces which arise in non-inertial reference frames (e.g., the centrifugal and Coriolis forces which appear in rotating reference frames). Fictitious forces do not possess reactions.
It should be noted that Newton's third law implies action at a distance. In other words, if the force that object exerts on object suddenly changes then Newton's third law demands that there must be an immediate change in the force that object exerts on object . Moreover, this must be true irrespective of the distance between the two objects. However, we now know that Einstein's theory of relativity forbids information from traveling through the Universe faster than the velocity of light in vacuum. Hence, action at a distance is also forbidden.
In other words, if the force that object exerts on object suddenly changes then there must be a time delay, which is at least as long as it takes a light ray to propagate between the two objects, before the force that object exerts on object can respond. Of course, this means that Newton's third law is not, strictly speaking, correct. However, as long as we restrict our investigations to the motions of dynamical systems on time-scales that are long compared to the time required for light-rays to traverse these systems, Newton's third law can be regarded as being approximately correct.