# Rotation- is axle or wheel rotating?

What determines if something is rotating? For example, if we have a spaceship with a fake gravity rotation thing, how do we know if the outer ring is rotating or if it is stationary and the inner axle is spinning? Normally we could just say its all relative, etc, but weather or not you feel gravity is determined by which one is spinning. So how can you decide? The outer one might is spinning relative to the center, but that doesn't mean it's really spinning (the center axle might just be spinning) , so why should I feel gravity? And if the outer ring is (presumably) heavier than the center, than why should it spin anyway? The motor would just spin the lighter center.

rcgldr
Homework Helper
Unlike linear velocity, angular velocity at any point other than the center of rotation involves acceleration, which can be measured and felt (force).

but thats just the point- which one is accelerating? what determines it?

russ_watters
Mentor
The answer rcgldr gave explained that: what determines it is that you can feel it.

Suppose I was incapable of feeling it. Now , there is no way to tell which one is spinning. I turn it on and watch as (from my perspective) the center axlis begins to spin. Why should I feel anything? To me, it seems as though I haven't moved at all. I turn it off. Now, how can you prove that the wheel isn't rotating? Sure, relatve to the center it isn't, and relative to that planet it isn't, but relative to something, it is. So why shouldn't I feel it? What does it have to be rotating relative to for me to feel it?

I actually think this is a good question, and to be honest I can't think of an answer off the top of my head, but I will think about this as I sleep tonight and maybe I will realize an answer by morning, or some bright person on here will post it.:)

Assuming you are in the "gravity ring" of the space ship, and want to test if the ring is spinning, you could do a number of things to determine if the gravity ring were rotating: Weigh something on a scale, throw something and watch its trajectory, swing a pendulum and observe perturbations, watch things fall. Spin up the ring until you pass out from too many gs or the ring tears apart from excessive force.

Gravity can be calculated as V2/r the square of the velocity (say meters per second) divided by the radius of the ring (meters) would give you your acceleration in meters per second squared. One gravity is about 32.2 feet (or 9.8 meters) per second squared.

Why in free space would there be any sense of gravity on a spinning ring? If you are accelerating, what is it in reference to? It would appear that there is something in the universe, a fabric of space, that provides a frame of reference (the http://en.wikipedia.org/wiki/Luminiferous_aether" [Broken]. Might have to ask a physicist or cosmologist.

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D H
Staff Emeritus
It certainly is not the luminiferous aether. Nor the Higg's mechanism. And it's not quite Mach's Principle as well. This has been a vexing problem for quite some time. Google the phrase "Newton's bucket".

Per relativity, velocity is relative. There is no preferred frame that lets one say "my velocity is X". The best one can do is say "my velocity relative to A is X." On the other hand, rotation, like acceleration, is in a sense absolute. Gyroscopes and accelerometers measure rotation and acceleration with respect to something external, but they do this in a purely local sense.

Dale
Mentor
2021 Award
Now, how can you prove that the wheel isn't rotating?
With a ring interferometer or a gyroscope. Those can be used to distinguish rotation from non-rotation without reference to anything outside.

sophiecentaur
Gold Member
If you were on this wheel then you could stand at the centre and try to pull an object on the periphery towards you with a string. Then do the same with an identical object which is diametrically opposite on the wheel. If the two forces are equal and opposite then I think you can conclude it is the wheel rotating around the centre.

Guys you are missing the point here....

If I'm strapped into a centrifuge, and I can see the axle about which it rotates, if the centrifuge starts spinning, from my perspective I appear perfectly still and the axle appears to be spinning. The same is true for the axle.

The question here is, why should one feel acceleration and not the other, if from either perspective one is rotating and not the other? Forget using measurements and equipment - that is not the point of this question. The point is, if I have no other reference point to decide which is rotating - me or the axle - why is it that only one of us experiences acceleration.

Just give this a moment's thought... the only way I can resolve this is to say you must measure rotation with respect to some privileged frame of reference...

D H
Staff Emeritus
Bingo. Even in relativity, rotation and acceleration are absolute in a sense. Gyroscopes and accelerometers are prima facia evidence of this.

Dale
Mentor
2021 Award
the only way I can resolve this is to say you must measure rotation with respect to some privileged frame of reference...
Yes, such privileged frames are called "inertial frames". All inertial frames are equivalent to each other, but they are not equivalent to non-inertial frames.

Btw, in GR the distinction between inertial and non-inertial disappears and the metric determines the physics of a given frame.

Hello. New guy here ^_^

In reality you are in a planet which you are rotating around a sun which is rotating around a galaxy so you your self are in the situation you describe.

So how can you tell? without a second reference frame you can't tell it's relative.

Also if its always there and it is constant and you grow up in it your body adapts to it so you wont even realise its there.

*EDIT* If you are in a "wheel" and run around in the direction of the wheel you will get lighter and against the direction you well get heavier.

Bingo. Even in relativity, rotation and acceleration are absolute in a sense. Gyroscopes and accelerometers are prima facia evidence of this.

I find all this profoundly interesting. Allow me to pose you, or anyone who wishes to answer it, another question.

Suppose from an inertial reference frame, the earth is rotating with a rate of 1.7 x 10-3 radians per second (period of 24 hours) in the clockwise direction. Now suppose I travel to the north pole, and place a simple spinning top, with a sufficiently large moment of inertia such that if I spin it at 1.7 x 10-3 radians/s it will be stable against gravity. I place this thing exactly at the earth's axis of rotation, and give it an angular velocity equal to and opposite the earth.

Relative to the earth, this spinning top has an angular velocity of -1.7 x 10-3 radians/s, but from our inertial frame, this top has zero angular velocity. Does the top fall down?

Dale
Mentor
2021 Award
So how can you tell? without a second reference frame you can't tell it's relative.
Hi JustinD, welcome to PF!

Yes, you can tell if you are rotating without comparison to a second reference frame. Simply use a gyroscope or a ring interferometer. These devices work completely locally and do not require an external reference.

D H
Staff Emeritus
Relative to the earth, this spinning top has an angular velocity of -1.7 x 10-3 radians/s, but from our inertial frame, this top has zero angular velocity. Does the top fall down?
You have a numerical error. 1.7x10-3 radians/s is one revolution per hour. The Earth is rotating at one revolution per sidereal day (3.93 minutes shy of 24 hours), or 7.292×10-5 radians/s.

Ignoring this numerical error, yes, the top will fall over.

Note that even if the Earth was not rotating the top would fall over. A top spinning at one revolution per sidereal day is spinning far too slowly. So, let's make the problem a bit more interesting. Instead of one revolution per day, or one revolution per hour, let's assume a planet rotating at a heftier rate -- say 100 radians/second. This planet will need to be made of unobtanium, of course, lest the planet's rotation tear the planet apart.

Now things are getting interesting in the case of a top positioned right at a pole. Counterspin the top at 100 radians/second and it will fall over. Even more interesting is making the top stationary with respect to the spinning planet. This top will not fall over.

Becuase one rotating object is solid throughout, the linear speed of points increasingly farther away gets faster. Suppose you are on said space station. Is the axle spinning or the station. Well, let's ponder both reference frames for a minute. Suppose the station is the thing that's really rotating, and the axle is not. From the axle-stationary reference frame, we see the station spinning. No problem there. But from the station-stationary frame, we see the axle spninning, but we also see the stars winging around like crazy. Could that really be happening? No. They would have to be moving way faster than the speed of light for that to be true.

So the way to tell is this: the correct rotational frame of reference is the one in which no object has a linear speed greater than C.

diazona
Homework Helper

Becuase one rotating object is solid throughout, the linear speed of points increasingly farther away gets faster. Suppose you are on said space station. Is the axle spinning or the station. Well, let's ponder both reference frames for a minute. Suppose the station is the thing that's really rotating, and the axle is not. From the axle-stationary reference frame, we see the station spinning. No problem there. But from the station-stationary frame, we see the axle spninning, but we also see the stars winging around like crazy. Could that really be happening? No. They would have to be moving way faster than the speed of light for that to be true.

So the way to tell is this: the correct rotational frame of reference is the one in which no object has a linear speed greater than C.
It's an interesting idea, but still, that doesn't uniquely select one reference frame. It just narrows down the set of reference frames that can be considered to be "correct" in your sense. Say the most distant objects observable are 10 billion light years away (order of magnitude ), then one of those objects traveling at the speed of light in the transverse direction would have an apparent angular speed of 10-10 radian per year. You could adjust your rotational velocity by less than that and still be in a reference frame where no distant object was moving faster than c, but supposedly if you had a rotational measuring device sensitive enough to detect such small angular velocities, you'd be able to tell that you were no longer in an inertial reference frame. Of course, no measuring device that sensitive exists in practice...

I don't know that there's any direct experimental evidence to confirm that such a small shift in angular velocity would switch you from an inertial frame to a non-inertial frame. But the idea that it might not seems rather weird and I don't really see how it could be compatible with relativity. (Who knows, maybe that's one of the wacky predictions that could come out of a quantized version of relativity, if/when we ever develop it )

That was basically the idea behind Mach's principle, by the way - that rotation is defined with respect to distant matter in the universe.

That 'fake gravity' itself is ur answer...if u r standing on the inner side of the outer wheel watching the axle, the fact that u r able to stand just like a person on earth suggests that the outer wheel is rotating w.r.t an inertial frame of reference producing centrifugal force......weigh an object whose mass is known and thereby calculate 'a',now u can determine the angular speed 'w=v/r' of the outer wheel w.r.t the inertial frame using the formula 'a=v^2/r '(r=distance of the object from the centre).....now calculate the angular speed , w2 of the axle w.r.t you..... if w2 is >w or<w then the axle is also rotating w.r.t the inertial frame of reference, if w2=0 both the axle and the wheel are being rotated together w.r.t the inertial frame of reference, and if w2=w, then either the axle is rotating at 2w in an dir'n opposite to the rot'n of the outer wheel or it is not rotating , w.r.t the inertial frame of reference. Now in the third case(w2=w) ,bring an electromagnet whose strength you can control, near the metallic surface of the axle and let it loose to get attached on the surface, now reduce the strength of the magnet such that its force of attraction reaches '4mw^2r'(here r=radius of axle) and slowly reduce it further, now if the magnet immidiately gets detached, it'd mean that the axle is rotating at 2w which creates a centrifugal force of '4mw^2r' thus detaching the magnet, and if the magnet doesn't get detached at all untill its magnetic prop. are removed, it'd refer that the axle isn't rotating w.r.t the inertial frame of reference.
This expt. is very time wasting, may be even unrealistic but it has to be done in order to know whether the axle is actually spinning.