Spining Problem

[Sebastian]

:confused: Hi , My friend asked me a question that i cannot seem to answer. Why does a spining body in space continue in its motion? Seemed like an easy question until he pointed out that the ends of the body are moving in a circle and are therefore accelerating in apparent violation of Newtons First Law of Motion. It also seems tha our gravitational theory has the same question if it is true that if a hole is made through the center of the earth a body dropped in would continue to accelerate forever. Can someone help me out?

[Tormod]

A spinning body in space spins because nothing is stopping it. Why it *began* spinning is a different question, and depends on what the initial forces were. But for all practical purposes, something spinning in (empty) space will keep spinning as long as there is no force acting upon it.

 

If the body is *not* spinning, it will not start spinning by itself unless an outside force (for example gravity) causes it to start spinning.

 

The point that "the ends of the body are accelerating" is a false assumption. The motion is constant, unless some force is acting upon it, which is then explained by Newton's laws of motion.

 

The hole in the Earth thing: If you made a hole through the earth, the object you dropped in would emerge on the other side, then fall back into the hole and emerge again on this side. Each time it would fall slightly shorter and eventually settle in equilibrium at the centre of the Earth.

 

This is a purely hypothetical situation, because given the motion of the Earth it is not certain that the object would not hit the edges of the hole (which would actually be a tube or tunnel) and thus slow down from friction.

[Sebastian]

So what you are saying is that the ends of the body do not accelerate? I don't have a problem with that except if the body in question is not a sphere but two shperes connected with a string and is set into spining motion. Does it go on for ever and if so why?:confused: :confused:

[Tormod]

So what you are saying is that the ends of the body do not accelerate?

 

I don't understand the question.

[Sebastian]

Let me make this easier to understand.

 

Two bodies of equal mass are linked by a string and set into a spining motion where the spining axis is in between the bodies at the center of the string. Its a couple.The two bodies are accelerating, right? So do they go on for ever or do they stop?

[ronthepon]

Let us remind our self of the modernised statement of newton's first law before we proceed.

 

In the absence of external forces upon a body, it does not experience any change in it's state of motion.

 

(I might say that this statement is not exactly worded ultra-rigidly)

 

So, let us look at a spinning body in space.

 

Now we must remember that for a body to move in a circular path, a centripetal force must be there, directed to the axis of rotation.

(Yeah, yeah, I know that you know this but please read on.)

 

In the string connecting two spinning bodies of equal mass, the tention of the string provides this force, in a sphere spinning all by itself in space, the force between the atoms of the sphere provide this force.

 

Point is that centrepital force is always there in any circular motion, and the moment this force dissapears the revolving bodies fly off at tangents.

 

This means that we cannot apply newton's first law because an external force is present on the bodies exhibiting circular motion.

[ronthepon]

Allright, and for the rest of the point, let me remind you that force can be applied for an infinite amount of time... however work cannot be done forever by a force.

 

That means that there cannot be displacement in the direction of a force forever.

 

In rotationary motions, the force is always perpendicular to displacement. So over a full cycle there is zero work done in all.

 

And in the hole-in-the-centre-of-earth problem, as long as the only force on the body is gravity (I mean no friction or whatever...) the total work will be zero over a full time period of oscillation.

 

The story is same for any other conservative force.

[Jay-qu]

The system will keep spinning due to its rotational momentum. Yes circular motion requries there to be a force radially inward. This is not in violation of any law, since the force acts in a perpendiclar direction to that of the motion, there is no work done and hence no need to consider energy in this problem.

 

As for dropping something through the center of the Earth. If the Earth was not moving and there was no frictional effects due to air, then its all a matter of simple harmonic motion. Gravitational potential energy is converted into kinetic energy then back to gravitational potential energy and so on indefinitely.

[Sebastian]

Thanks a lot I think i have it cleared up now

[Webbly]

Slight change of subject, but seems a good place to ask (point me to a thread if I missed it).

 

A body in deep space: how does it "know" it's spinning?

 

For example, if the body is an astronaut, his spaceship explodes and he's violently sent hurtling off in his space suit (so we can discuss his demise in the seconds that follow, if need be), and we define him as spinning relative to stars/galaxies, on an axis within his body.

 

Though common sense says centripetal and centrifugal forces operate on his body - in deep, really deep, space, with respect to what?

[InfiniteNow]

A body in deep space: how does it "know" it's spinning?

Basically, you would need to rely on visual cues... "Hey, why does that planet keep passing in front of my face from left to right?"

 

It's a bit like skydiving... you really wouldn't perceive yourself falling if it weren't for the wind brushing past you turbulently (unless you have a SUPER sensitive inner ear and are highly attuned to the cillial reactions to the ear fluids... but I'm pretty sure that wouldn't be a factor out in space).

[Jay-qu]

So you think we wouldnt be able to tell? What about the prophesy, it is spinning in order to keep our artificial gravity, so if we can tell its spinning 'relative' to something do we just fall off the floors ;)

[Webbly]

You'll have to excuse me for not being sure how to precisely put the question, and so (with respect to replys above) may I restate it with my example pushed a bit harder?

 

Spin a body (or anything) on Earth and it eventually disintegrates if the rotation becomes fast enough. Our astronaut turning on some bodily axis would be fatally affected as RPMs increase.

 

On Earth this seems obvious and common sense, but transport the situation into deep space and with respect to what is the astronaut rotating (not to mention that spot on the planet's surface, that happens to be scribing some odd spiral itself)?

 

If the answer is he's spinning wrt our galaxy, communities of galaxies, all the way up to the universe, then I'm still wondering what forces define him as spinning (that make his body try to tear apart) compared to a body 'at rest'?

 

To make it worse (for me) consider two bodies: one spinning, the other not. The non-spinner sees the other spinning. The spinner finds the non-spinner in orbit about him (I'm having a paradox moment here!).

 

The answer might be high school physics 101, and if so I was certainly asleep that day. So I'm fascinated. Someone point out the obvious.

[CraigD]

A body in deep space: how does it "know" it's spinning?

Restating Webbly’s astronaut example slightly, if an astronaut observes that nearly all distant objects appear to be orbiting him at the same rate, how can he tell he is rotating around his center of mass, rather than those distant objects revolving around him.

 

Common sense experience – Ocam’s razor – suggests that this rotation is the simpler explanation. However, the astronaut need not rely on common sense, but can conduct the following simple experiment: assuming he has a small, detachable object – let’s say a coin – he can clasp it in his hand, extend his arm, and gently release it. If it remains near his hand, repeat the experiment, extending his arm in a 90° different direction. If it still remains near his hand, he’s not rotating. If it appears to accelerate away from his hand, he is rotating, and the apparent acceleration is not of the coin, but of his hand.

[Webbly]

Thanks CraigD for picking up on this. I really need to do some revision to help put the question more intelligently, but haven't had time.

 

You have probably given a definitive answer to how respondents so far have interpreted this question, and looking back it was an interesting question, but not the one I intended. :)

 

Can we try another direction, another attempt at the intented question? And let's lose the astronaut.

 

-------

 

In deep space, again. A sphere is "rotating around its center of mass" because we say it is. The universe is happy with this, all laws being observed.

 

Increase rotational speed and - how do you say it? (centrifugal forces begin to exceed centripetal forces?) the sphere begins to disintegrate. (Kindly correct that if I've misused the names, concepts and natures of forces).

 

The question is "what absolute authority defines not only this state (the body is about to fly apart) but even the fact that it is spinning and has to fly apart"?

 

Previously I said 'how does x know it is spinning' - which simplification was meant to ask 'wrt what is it spinning that would create rotational stress?'

 

Or, 'what universal laws define anything as spinning?'

[CraigD]

"what absolute authority defines not only this state (the body is about to fly apart) but even the fact that it is spinning and has to fly apart"?

…

Or, 'what universal laws define anything as spinning?'

Newton’s first law of motion, which states that an object in motion travels in a straight line unless acted upon by an outside force.

 

In Webbly’s example, the “object in motion” is any small piece of the spinning body. The force is due to whatever “adhesive” is holding it together (eg: the strong nuclear force, glue, gravity, depending on its size). A force that causes an object to move in a circular path is called a centripetal force, and derives from the first law via simple geometry.

 

If the speed of the piece ([math]v[/math]) increases such the maximum force that can hold it together ([math]F[/math]) in a sphere (or other shape) with radius [math]r[/math] such that [math]F \le \frac{v^2}{r}[/math], and whatever is holding it together cannot “reconfigure” itself to have a larger [math]r[/math], the body will “break apart” - the force it’s ”adhesive” exerts on the piece will become effectively zero, and, per Newton’s first law, the piece will travel in a straight line, away from the center of mass of the body.

 

I wouldn’t call Newton’s law an “absolute authority”, more of an “empirical rule” – though a very good one. Why physical reality follows it is a very deep and currently incompletely answered – with what is answered having a reasonable likelihood of being badly wrong - question, full of entities like Higgs bosons that I only poorly understand.

[Webbly]

CraigD, thanks again for a very precise breakdown of the question. Probably it cannot be explained any further - ie., what you haven't answered is what I'm not capable of asking.

 

I hope to return after a bit of heavy reading and actually frame my real puzzle intelligently - unless it is one of those useless wonderings, like "What was before the big bang?"

 

Answers like this quote in a similar forum suggest I had better lay off till I know more.

 

The Milky Way is turning, and from where we are, 30,000 light years from the Galactic centre, is taking our Solar system with it at half a million miles per hour in the first direction to establish stage one of the formation of 'Gyrotic' Gravity.

 

Within this system, the planet Earth is speeding in orbit around the sun at 78,000 miles per hour in a different direction to make up stage two, and within both these systems, the Earth is spinning on its own axis at 1,000 miles per hour in yet another direction to make up the final stage of the gyro and produce Gyrotic Gravity. Gravity that not only holds together those heavenly bodies, but gravity that escapes.

 

It can escape because it is being continually produced.

 

With all the nine planets contributing with their own individual piece of gyrotc gravity, our entire Solar system, and the billions of other Solar systems which contribute theirs, create a massive Gyrotic gravitation field, not only within the confines of the hundreds of billions of galaxies in the Universe, but well into the dark matter that surrounds them.

 

Thanks all, but feel free to bite into that if it takes your fancy.