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I read in a book (Fundamentals of Mechanics by IE Irodov) that inertial forces do not obey newton's third law. I am unable to imagine and get this in my mind. It states:

"Inertial forces are not caused by the interaction of bodies but by the properties of non inertial refrence frames themselves. Therefore inertial forces do not obey Newton's third law of motion."

Now I am having a hard time understanding and believing the sentence. Why is this true?

Qmechanic
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Aditya Pandey
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    What is it you do not understand? Newton's third law states: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. As fictitious forces are not exerted by anything, how could they ever obey that law? – ACuriousMind Sep 08 '14 at 15:09
  • How can gravitational force be considered as fictiious force? – Aditya Pandey Sep 08 '14 at 15:13
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    Who said that gravity is fictitious? (Hint: It isn't.) – ACuriousMind Sep 08 '14 at 15:15
  • Possible duplicate: http://physics.stackexchange.com/q/81191/2451 – Qmechanic Sep 08 '14 at 15:16
  • @ACuriousMind It was Einstein who said that gravity is a fictitious force. See https://en.wikipedia.org/wiki/Fictitious_force#Gravity_as_a_fictitious_force . – Red Act Sep 08 '14 at 15:26
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    @RedAct: Ah, that might explain the confusion here. Nevertheless, in the elementary mechanics context that a book called "Fundamentals of mechanics" most probably has, gravity is not fictitious. – ACuriousMind Sep 08 '14 at 15:27
  • Like all the inertial forces gravitational force also depend on mass. And that book contains Relativistic Kinematics and Dynamics also. – Aditya Pandey Sep 08 '14 at 15:35
  • @ACuriousMind: Gravitation in a Newtonian framework IS a pseudo-force. The force of gravitation that we feel is actually the force of the ground that keeps us from moving in a free falling trajectory, which would be the real inertial system in the vicinity of a gravitating body. The simple fact is, that the surface of Earth is NOT an inertial system. That we have been treating gravity as a force, rather than an acceleration is a historical artifact, which was corrected by Einstein when he introduced GR. – CuriousOne Sep 08 '14 at 17:03
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    @CuriousOne: Hmm...what about $F = G \frac{m_1 m_2}{r^2}$ is fictitious? It is true that GR treats gravity as fictitious, but I cannot see how that could be true in a Newtonian framework - put two (big) masses into space. They attract. That force is surely not fictitious, as it can be observed in (Newtonian) inertial frames. – ACuriousMind Sep 08 '14 at 17:10
  • @ACuriousMind: Everything about it is fictitious. A body moving freely in the gravity of another body doesn't experience ANY force. It experiences an acceleration of the size a=GM/r^2. The force that you reference can only be observed by holding the body in a FIXED reference frame relative to the gravitating body, and then it's actually the holding force, not the force of gravity. Newtonian mechanics doesn't define "inertial" as "fixed". It defines it such that for every force there is an equal counterforce at THE SAME point. In case of gravity there isn't. – CuriousOne Sep 08 '14 at 17:17
  • @ACuriousMind: Another important thing to keep in mind is that pseudo-forces are perfectly real and lethal. Pseudo or fictitious does not mean "non-existent". Think about the pseudo-force in a car during an accident. The rapid deceleration is a very real physical effect that will lead to very real physical trauma, even though it is "just" a pseudo-force which acts trough the physical force of the dashboard slamming into the human body, which is actually doing nothing but to continue its perfectly Newtonian trajectory based on its momentum and inertia. – CuriousOne Sep 08 '14 at 17:26
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    @CuriousOne: That rapid deceleration is a real force, not a fictitious force. It is present in all frames, including inertial frames. Fictitious forces disappear in inertial frames. A force that is still present in an inertial frame is a real force. As far as gravitation is concerned, it depends on context (and student education level). Gravitation is a real force in Newtonian mechanics, but it's a fictitious force in general relativity. – David Hammen Sep 08 '14 at 19:09
  • @DavidHammen: "Fictitious forces disappear in inertial frames." Which is exactly what gravity does. There is no gravity in the center of mass system of the ISS. What upsets most students is that the surface of Earth is simply not an inertial system and Newton's laws simply don't apply around here. One has to be in free fall to experience what Newtonian physics really feels like! – CuriousOne Sep 08 '14 at 19:36
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    An ISS-based frame is an accelerating frame, and hence not an inertial frame (Newtonian context). There are fictitious forces in that frame (and gravitation is not one of them in a Newtonian context; gravitation is a real force in Newtonian mechanics). A frame fixed with respect to a non-rotating rogue planet between galaxies is an inertial frame in Newtonian mechanics, but not in general relativity. Do not mix and match inertial frames between Newtonian mechanics and general relativity. The two theories have rather different concepts of what constitutes an inertial frame. – David Hammen Sep 08 '14 at 19:56
  • Related https://physics.stackexchange.com/questions/405791/why-do-pseudo-forces-not-obey-newtons-third-law/804884#804884 – Nikos M. Mar 03 '24 at 22:01

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The short answer: Inertial forces don't obey Newton's third law. There are no inertial forces in an inertial frame of reference, and that's where Newton's third law applies.

Consider two observers of some events. One of the observers is inertial, the other is rotating at a nonzero rate with respect to the first. Suppose the inertial observer sees an object moving along a straight line trajectory at a constant velocity. The inertial observer will correctly deduce that the object is subject to zero net force.

The rotating observer will see the object moving along a curved trajectory, possibly with a non-constant speed. If that observer insists on explaining that observed motion via F=ma, that perceived acceleration can only be attributed a non-zero external force. The problem: There is no third law counterpart to that force. It's solely a consequence of (mis)using Newton's second law to explain that motion.

Let's add a third non-inertial observer who is rotating differently than the second one. This observer will also see a non-zero acceleration, but different from that of the second. That means the force is different from that inferred by the second observer.

One way to look at fictitious forces is that they are figments of the observer's imagination. They don't exist. Another way to look at them is that they are a mere misapplication of Newton's second law. Newton's second law is properly a concept that applies in inertial frames only.

A third way to look at fictitious forces is that while they might be figments of ones imagination, they are extremely useful figments. Just try to model the weather from the perspective of a non-rotating, non-accelerating frame. Good luck! On the other hand, this task, while difficult, is doable when viewed from the perspective of a frame rotating with the Earth.

David Hammen
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