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Someone told me that it is not inertia, but I think it is inertia, because it will rotate forever. In my understanding, inertia is the constant motion of an object without external force. Am I wrong?

Tanner Swett
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enbin
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  • It is external torques that cause an object to rotate (change angular momentum), as external forces are only responsible for moving the center of mass. An offset force happens to produce torques as a secondary effect. – John Alexiou Jul 17 '19 at 14:36
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    What did the other person say it is? – Andrew Morton Jul 17 '19 at 14:54
  • @ja72 So it's going to rotate forever. Isn't that inertia? – enbin Jul 17 '19 at 15:29
  • @AndrewMorton I was told that rotation is not inertial because it is not an inertial system. – enbin Jul 17 '19 at 15:35
  • @enbinzheng - no it is angular momentum and the conservation of it. Think of superfluid (no viscosity) rotating, it will continue to rotate forever even though there is no "inertia" associated with a fluid (or any non-rigid body). – John Alexiou Jul 17 '19 at 16:22
  • @ja72 What do you mean there's no inertia associated with a fluid? The Reynolds number is a ratio of inertial forces to viscous forces in a fluid, and fluids definitely have non-zero Reynolds numbers. – JMac Jul 17 '19 at 18:42
  • @JMac - Inertia defined as the value that transforms rotational motion to angular momentum is not defined for a fluid. For a rigid body $L = \mathrm{I}, \omega$ describes angular momentum with $I$ being the inertia of the body. For a fluid, angular momentum is $L = \sum_i r_i \times (m_i v_i)$ with no way to factor our the motion parts (in general). – John Alexiou Jul 17 '19 at 19:44
  • @ja72 "Inertia defined as the value that transforms rotational motion to angular momentum" I don't know anyone that uses "inertia" that specifically, and I think it's confusing to use it that way here instead of the general meaning of inertia. – JMac Jul 17 '19 at 19:48
  • @JMac - https://en.wikipedia.org/wiki/Moment_of_inertia#Definition – John Alexiou Jul 17 '19 at 20:57
  • @ja72 https://en.wikipedia.org/wiki/Inertia Inertia and moment of inertia are different things. You said "there's no inertia associated with a fluid"; which is obviously pretty confusing because fluids definitely have mass and resist changes in velocity. – JMac Jul 17 '19 at 21:00
  • @JMac - in the context of this question "inertia" => "moment of inertia" since we are talking about rotations. – John Alexiou Jul 17 '19 at 21:05
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    @ja72 I highly disagree. I think that's the entire crux of the question. Equating the two without explaining that "inertia" and "moment of inertia" are different things might completely neglect why OP got into this conversation in the first place, and may only add to the confusion. OP only ever talks about "inertia" so assuming that he really means "moment of inertia", without explaining that they are different, is likely not going to help them. – JMac Jul 17 '19 at 21:11
  • I think the word "forever" must be used with care in physics/mechanics, here it will move"forever" if no force is applied (1st Law of Newton, as some answer pointed it out). A real system will never run forever due to friction forces, Joule's effect, the laws of thermodynamics about closed system... You may improve your question by formulating the correct hypothesis: "Assuming rigid body with perfect linkage, and no friction ...". – Cailloumax Jul 18 '19 at 08:05
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    @knzhou I feel like your edit to the title made it much less clear than it was before. Now it sounds like the title is asking, "How long does inertia keep an object rotating? Forever? How about something else?" The previous title was pretty clear, but I just submitted a suggestion for a third title ("What causes a rotating object to rotate forever without external force—inertia, or something else?") – Tanner Swett Jul 18 '19 at 14:27
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    @TannerSwett Sure, that's fair; I voted to approve the edit. – knzhou Jul 18 '19 at 14:39
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    Nobody seems to have noted (so I may be in trouble :-) )that a rotating object in one frame of reference is a stationary object in a specific other frame of reference. "Just because" this requires the whole of the rest of the universe to be rotating relevant to it does not mean that it is not stationary. ||| THIS FEELS WRONG :-) -> If I am in "empty space" with another object and it is "spun up" by eg "thrusters" then it experiences ongoing rotational forces and I do not. ... – Russell McMahon Jul 19 '19 at 07:56
  • ... If instead I am spun up along the same axis but in the opposite rotational direction I experience rotational forces but in both cases see the same result. Summat aglae with my reasoning, but ... :-) – Russell McMahon Jul 19 '19 at 07:56
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    @Cailloumax The ideal state described by Newton's first law does not exist in fact. – enbin Jul 19 '19 at 16:53

4 Answers4

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Is it inertia that a rotating object will rotate forever without external force? Someone told me that this is not inertia [...]

Well, sort of - it’s somewhat correct to say it is inertia, and somewhat correct to say it isn’t. One has to be precise with language! But there is some truth to what you were told.

“Inertia” generally refers to the tendency of objects to continue moving in a straight line with a fixed velocity unless an external force is applied to them. It is basically a single word that encapsulates Newton’s first law of motion. It is a very fundamental law of nature, and at some level, no one really knows why it’s true.

The different parts of the rotating object are definitely not moving in a straight line, and it’s not the case that no forces are acting on them. So there is more than just inertia at play.

What is happening with a rotating rigid body is that each part of the body “wants” to maintain its fixed velocity according to the law of inertia, but the rigidity of the body is preventing it from doing so (since the pieces of the body have different velocity vectors so with fixed velocities they would all fly off in different directions). At the microscopic level, each piece of the body is applying forces to the adjacent pieces. Those forces are causing those adjacent pieces to change their velocity, according to Newton’s second law of motion. The end result of this highly complicated process is surprisingly simple: the body rotates. But the underlying cause is more than just inertia.

Now, I said it’s also somewhat correct to say that it is inertia that’s making bodies keep rotating. This is because there is also a rotational analogue of inertia that in informal speech among physicists might still be referred to as “inertia” (although calling it rotational inertia is more appropriate, and it will also commonly be described under the terms “moment of inertia” or “conservation of angular momentum”, or even more fancy terms like “rotational symmetry of space + Noether’s theorem”, although each of these terms describes something a bit more complicated than just rotational inertia). This rotational inertia is the tendency of rotating rigid bodies to continue rotating at a fixed angular velocity in their center of mass frame, unless a torque is applied to them.

Rotational inertia differs from ordinary “linear” inertia in that it is a derived principle: it can be derived mathematically from Newton’s laws of motion, so in that sense it has (in my opinion) a slightly less fundamental status among the laws of physics. Rigid bodies don’t “want” to keep rotating in the same fundamental sense that particles “want” to keep moving in a straight line with a fixed velocity - they do end up rotating but it’s because of a process we understand well and can analyze mathematically (starting from Newton’s laws), rather than some mysterious natural phenomenon we observe experimentally and accept as an axiom without being able to say much more about why it’s true.

GenlyAi
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    «“Inertia” generally refers to the tendency of objects to continue moving in a straight line with a fixed velocity» It is the Merriam-Webster definition but is it the true definition of the scientific concept ? Wikipedia defines Inertia as «The resistance, of any physical object, to any change in its velocity.» which covers both the linear momentum and angular momentum. – zakinster Jul 17 '19 at 12:38
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    @zakinster But a rotating object consists of parts which are constantly changing velocity. It's not clear how that definition would apply here, because angular velocity and velocity are two fairly distinct concepts. – JMac Jul 17 '19 at 14:24
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    @zakinster as I said, the constituent parts of a rotating body are constantly changing their velocity, hence this does not fit Wikipedia’s definition. – GenlyAi Jul 17 '19 at 17:03
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    In general I would not immediately assume that a Wikipedia definition is a "true definition" of any concept, scientific or otherwise. – Lee Mosher Jul 17 '19 at 20:06
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    @LeeMosher good point. But Wikipedia gets it right on this particular occasion. – GenlyAi Jul 17 '19 at 20:19
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    Moment of inertia and angular momentum are two different things. Moment of inertia is the angular analog of mass, while angular momentum is the angular analog of momentum. – Acccumulation Jul 18 '19 at 17:05
  • Without external force, the rigid body rotates all the time, which is inertia. – enbin Jul 18 '19 at 22:32
  • @enbinzheng that is circular reasoning. If you are defining inertia as the thing that causes rotating bodies to rotate indefinitely, then yeah, it is inertia. But inertia has already been defined by other people, you can’t unilaterally assign it the meaning that you decided is the correct one. I suggest that you re-examine your assumptions and try not to get fixated on your (slightly misguided, I think) idea of what inertia is. – GenlyAi Jul 18 '19 at 23:07
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    In a counter-factual version of physics in which objects do not continue moving when no external force is applied (i.e., there is no such thing as inertia) then, as a direct consequence, objects would also not continue rotating when no external force is applied. To me, that says that it is indeed inertia that causes rotational inertia. – Harry Johnston Jul 19 '19 at 03:27
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    @HarryJohnston: Inertia is so fundamental to our universe that I think your counterfactual version of physics would have very little common with ours. That hardly justifies saying that inertia is "what causes" everything we observe. – ruakh Jul 19 '19 at 03:45
  • @ruakh, well, I'm taking a Newtonian-style-mechanics point of view, of course; things like quantum field theory and GR are out of scope. – Harry Johnston Jul 19 '19 at 04:04
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    ... but I suppose that you could derive the conservation of linear momentum from the conservation of angular momentum just as well as the other way around, so I guess there's no particularly objective reason to say which is cause and which is effect. – Harry Johnston Jul 19 '19 at 04:10
  • @HarryJohnston to be clear, I’m not saying that inertia has nothing to do with it. Of course a world without inertia would likely also not have bodies that rotate indefinitely. But an important point that I was trying to make is that the explanation for why bodies rotate requires more than just inertia. Thus saying “it is inertia” is misleading and oversimplistic, and suggests that the person saying it hasn’t thought the whole chain of causality through. – GenlyAi Jul 19 '19 at 05:38
  • @GenlyAi, fair enough, I'd overlooked that. +1. – Harry Johnston Jul 19 '19 at 05:41
  • I suppose the other forces at stake are the forces that make the solid a solid, so gravity + the other 3 forces that keep atoms together+ maybe some quantum stuff. I'm no physicist, but a bunch of forces acting against inertia would probably warm up the object (high risk claim, if I'm wrong, it's probably here). An object at some temperature will emit radiation. With a loss of energy, there's a loss of mass, which would lead to the conclusion that objects cannot rotate indefinitely because they will evaporate sooner or later. – Andrei Jul 19 '19 at 13:05
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    @Andrei the earth has been rotating for an awfully long time without evaporating... anyway, the heat death of the universe and other exotic physics topics aren’t really relevant to the question, which is about Newtonian mechanics. – GenlyAi Jul 19 '19 at 18:22
  • @GenlyAi I mean that both rotation and linear motion are inertia. So I didn't say that only rotation is inertia. – enbin Jul 20 '19 at 06:49
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At its most basic, an object will rotate forever for the simple reason that there is no preferred direction in space.

Emmy Noether's theorem of 1918 explains how various conservation laws arise from from differentiable symmetries. It is a mathematical theorem, not a physics theory. Because of this mathematical certainty, it is one of the most important theorems in physics.

Noether's theorem explains how the conservation of angular momentum (rotation) is required on the assumption that rotation does not change the laws of physics. Similarly, energy is conserved if time does not change the laws, and conservation of linear momentum is caused by the absence of a preferred location.

As these assumptions have always been observed to hold, this gives a very strong proof for the conclusions (the conservation laws).

aniline hates nazis and pedos
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hdhondt
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    Is that "yes" or "no" to the question? – RonJohn Jul 17 '19 at 13:36
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    it is called conservation of angular momentum, as far as rotations go, one of the three strong conservation laws, energy ,momentum, angular momentum. They are called laws, because they are like axioms,seen to be to be true in data and thus the theory developed for mechanics incorporates them with Noether's theorem. – anna v Jul 17 '19 at 16:31
  • @RonJohn When classroom physics meets fundamental physics, simple yes or no questions rarely have simple yes or no answers. – Schwern Jul 17 '19 at 21:30
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    @Schwern I didn't ask for only "yes" or "no". The GenlyAI answer, for example, said both "yes" and "no". – RonJohn Jul 17 '19 at 21:33
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    @RonJohn It's a YES. Angular momentum is conserved. – hdhondt Jul 17 '19 at 23:26
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    @hdhondt if it’s a YES, how is it that nowhere in your answer or clarifying comment do you mention the word “inertia” even once? The question you’re answering with a YES was “Does inertia keep a rotating object rotating forever, or is it something else?”, so I find this quite strange. Your answer is interesting and I would like to see the idea developed further in a way that relates it to what OP asked about, but it seems to me that either you’re answering a different question from what was asked, or the answer is a non sequitur. – GenlyAi Jul 18 '19 at 05:13
  • Your answer uses three different verbs to explain the derivation from Noether's theorem to the laws of conservation: "is required", "is" and "is caused by", each having different implications. My (admittedly limited) understanding of Noether's theorems is that "is required" is likely the most correct implication of the relation between these laws and the theorem. – RBarryYoung Jul 18 '19 at 15:08
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As Newton stated with his 1st law, an object without a force acting on it will keep moving with the same speed and direction. This is also known as the law of inertia. Inertia is the tendency of an object to resist acceleration. This is because no force is acting on it to affect acceleration.

For rotational motion, the version of this is the moment of inertia which is similar, but about the tendency to resist angular acceleration.

So it is inertia (the moment of inertia if rotation). It keeps rotating at constant angular frequency since it resists a possible change out of nowhere.

KingMongolian
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  • Every particle of a rotating body does experience a force, which makes it accelerate towards the center of rotation. Those internal forces come from the fact that the internal stress in a rotating body is not uniform. The gradient of the stress tensor is equivalent to a distributed force acting on the body. The resultant of these internal forces over the whole body is zero, of course. The stress field is also what makes a body break apart, if you spin it too fast! – alephzero Jul 18 '19 at 21:22
  • OP encountered someone who's into semantic humbuggery. This doesn't say anything the other answers don't; it's just better syntax, +1. – Mazura Jul 18 '19 at 22:25
  • @Mazura What does OP mean? – enbin Jul 21 '19 at 06:43
  • @enbinzheng - 'original poster' : you – Mazura Jul 21 '19 at 22:17
  • @Mazura Isn't it inertia that a rotating object keeps rotating when it is not acted by external forces? – enbin Jul 22 '19 at 05:42
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Massive objects spin due to gravity. Intrinsic Spin (natural spin) which is a function of the planet mass and density.

“If the energy that creates the motion is part of the system and not applied externally then it will spin indefinitely.”

Gravitational Angular Velocity (GAV) is an intrinsic property of a planet or a very massive object where the influence of gravity is noticeable. Not to be confused with artificial rotation like spinning a ball, spinning a fidget spinner, or any type of rotation not related to gravity.

GAV[intrinsic property] = f(mass, density)

There are other forces of nature that may contribute to the slowing down or speeding up of a planet rotation like earthquakes, being hit by a meteor, tidal locking, etc., and these events can be considered as very small perturbations to the system.

Once the relationship is established, the below can be derived.

Rotational Energy Density (E/V) - as a function of “mass & density” and input to the Stress-Energy Tensor

Angular momentum (J) - as a function of “mass & density” and input to the Kerr Metric

Follow the link:

PLANETARY ROTATION (SPIN)

Randy Evangelista
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