If all motion is relative, what is Earth’s rotation relative to? Call it x. And if you took x away, would the Earth still rotate? For example, would you still be a tad lighter at the equator? If yes, how, if all motion is relative?

Motion in inertial frames of reference is relative - that means the part of Newton's laws that says once you put an object in motion, it stays in the same motion unless an external force acts on it - motion like that (without forces added, that is) is relative. Such motion has no acceleration. Now, it appears that rotation is such a motion, but remember that acceleration is defined as a change in the velocity vector, which has both magnitude and direction. Change the direction of motion, and you have acceleration. Since the motion of every particle of the earth, except an infinitely small point at the center, is constantly changing direction, the earth's surface is accelerating. The force that causes this is rotational inertia, but (somebody correct me if I am wrong, please) this inertia is constantly decreasing by an infinitisimal amount as it is used up to cause acceleration - maybe I got something wrong there, but it is a start. Someone else can probably explain it better. Somebody help!:D
Aaron

Rotation is absolute. Rotation induces ficticious forces -- and ficticious forces mean a frame is not inertial. You can build an apparatus in a closed room (a Focault pendulum) to measure the rotation of the earth.

- Warren

If all motion is relative, what is Earth’s rotation relative to? Call it x. And if you took x away, would the Earth still rotate? For example, would you still be a tad lighter at the equator? If yes, how, if all motion is relative?
<HR>
First, if we look at a cross-section of the earth cut through the axis of rotation, we would find the Earth is an ellipse. The length b, through the Earth's axis of rotation, is shorter than the length a, which is through the equator. If we are standing at the equator, there is more mass between us and the center of Earth than there is if we stand at the northern axis of rotation, (which actually wobbles). If anything, we will weigh more at the equator than we do at the northern pole. The centripetal force acting against gravity on Earth is negligible, but calculable. I suppose if Earth was a hollow sphere, we could measure this force quite easily from the inside walls.

Second, if we look at rotation from the axis, the axis does not actually move. It is a single line of one dimension. The tangential motion of rotation is relative to the axis and everything around it--everything in the Universe--except perhaps a moon in perfect orbit around a planet, synchronized perfectly with the rotation.
There is not a true reference frame for an object in circular motion, because it is under constant acceleration. The ficticious forces Warren mentions are centripetal force, centrifugal force, gyroscopic force, gyroscopic precession, and more. These skew the reference frame from relativity. This makes the reference frame of Earth, and any object in circular motion non-inertial. Relativity does not deal with ficticious forces in a non-inertial reference frame. (I hope that's right) I think that is what Warren meant to say below.



<b>Rotation is absolute. Rotation induces ficticious forces -- and ficticious forces mean a frame is not inertial. You can build an apparatus in a closed room (a Focault pendulum) to measure the rotation of the earth.</b>

Originally posted by chroot
Rotation is absolute. Rotation induces ficticious forces -- and ficticious forces mean a frame is not inertial. You can build an apparatus in a closed room (a Focault pendulum) to measure the rotation of the earth.

OK, that makes sense. So rotation is not relative motion per se. We need not be rotating with respect to anything to measure rotation using a Focault pendulum. And if all motion is relative, then that means that rotation is not motion per se, right?

The other comments are interesting too. Thanks!

Originally posted by zanket
And if all motion is relative, then that means that rotation is not motion per se, right? Never thought about that... good catch:)

I'd say that the motion of a single atom involed is still relative. Its apparent velocity will appear to change as your velocity changes.

Rotation of an object limits the frame of reference to the center of the object though.

So I'd guess that it depends on the way you look at it.

This was a good string.

One note is the fact that rotation is a form of acceleration and it results in a force of acceleration.

The interesting note is that where F=ma requires continual expenditure of energy rotation does not, perse.

Makes one wonder why virtually everthing in nature is linked to rotation.

From sub-atomic to gallactic motions. Perhaps the Universe itself, although it would apear we have no way of measuring that potential motion.

Originally posted by MacM
The interesting note is that where F=ma requires continual expenditure of energy rotation does not, perse.
Well, F=ma doesn't apply to non-inertial (i.e. rotating) systems.

- Warren

then that means that rotation is not motion per se, right?
<HR>
Circular motion is most certainly motion, or tires couldn't propel your car at a relative speed. Interesting isn't it? We talk about relative velocities on the surface of a planet that is round, and always in motion. It depends on the scale of the reference frame, doesn't it? I can make a really close to flat spot in pretty close to a vacuum, but gravity is still at play on Earth. The best reference frame is space. There, an inertial reference frame is pretty close to perfect. But, in truth, if we are orbiting Earth, it is still a non-inertial reference frame. How far away from the Sun and Earth would we have to go to have a true inertial reference frame? There isn't one. It's an idea. Circular motion doesn't fit into an inertial reference frame, but it's real. It's motion. It's relative, but relativity doesn't deal with it.

Whoever said "all motion is relative?" The ONLY motion that is relative is unaccelerated, uniform motion in a straight line.

Rotation is not relative.
Acceleration in general is not relative.

As I've said before, you can recognize that velocity is relative because it doesn't appear in Newton's laws; F=ma has no dependence on velocity. Acceleration, however, is NOT relative.

- Warren

The ONLY motion that is relative is unaccelerated, uniform motion in a straight line.
<HR>
I understand this, Warren. And when we calculate velocity, it is important. But, in the real world, there is almost nothing that fits into an inertial reference frame. It is not wrong for me to say, the Earth's surface is moving at x rate relative to the surface of the moon.

This is again, a very strict definition of terms. Just because relativity doesn't deal with circular motion, doesn't mean the speed of a gear in a transmission doesn't have relative speed to another, or that it is not in motion.

We don't have to use relativity to define circular motion, or the relative speed of a saw blade to the wood we are cutting.

Include General Relativity here.

Didn't Einstein make the point that it wouldn't be correct to call acceleration absolute motion because we can do away with it by assuming that a specially formed field of gravity exists there instead?

Originally posted by Natural
Didn't Einstein make the point that it wouldn't be correct to call acceleration absolute motion because we can do away with it by assuming that a specially formed field of gravity exists there instead?
No.

- Warren

Originally posted by Andre
Furthermore my textbook says that F=ma is an universal law, also applicable to rotations.
Inside a train going around a curve, a ball will fly to the outside wall of the train without anyone applying any forces to it. F=ma works if you assume ficticious forces and solve using them. I wanted Mac to realize that ficticious forces must be introduced to apply F=ma to a rotating system.

- Warren

Rotation is relative to the universe as a whole. If Earth was the only thing in the universe, it wouldn't make sense to say it was rotating... or would it? Maybe we would still experience forces such as centrifugal force, but maybe we wouldn't. The issue is almost a philosophical one.

You may want to look up "Mach's principle".

It was Mach I had in mind when posting this question. I like chroot’s answers here. It’s hard to believe that the Earth could depend on other bodies for its centrifugal force to be felt.

My stab at an explanation: Gravity squeezes the Earth towards a central point. A bullet fired parallel to the ground partially orbits the Earth. If given sufficient velocity the bullet would orbit the Earth and be weightless. The bullet is not orbiting the Earth so much as it is escaping movement towards the central point. The Earth provides the gravitational field, and the bullet orbits the center of the field.

When the Earth rotates, its surface atoms likewise partially orbit the central point. The faster we on the surface revolve around the point, the more weightless we feel (in principle, assuming the Earth remained a perfect sphere). The Earth is rotating relative to its gravitational field. The field indicates up & down, and thereby provides a reference for rotation. You know a planet is not rotating when its escape velocity is constant from all points on its surface.

If Earth was the only thing in the universe, could you determine if it was rotating? If a rocket could still be launched to orbit the Earth, then the answer must be yes.

Now is rotation relative to the universe as a whole? My intuition says no, and says that any body that presents the same face to another body as it revolves around it, like the Moon does the Earth, is not rotating. But I’ll have to ponder it some more.

chroot: F=ma works if you assume ficticious forces and solve using them.
What the heck are "fictitious forces"? F=ma is a basic law of science and it is universal. No assumption is necessary. No fiction is involved. Do your homework.

zanket: If Earth was the only thing in the universe, could you determine if it was rotating? If a rocket could still be launched to orbit the Earth, then the answer must be yes.
If earth was the only thing in the universe would it even BE rotating? How did the earth start rotating in the first place? All the planets, and the sun rotate. Why is that?

What the heck are "fictitious forces"? F=ma is a basic law of science and it is universal. No assumption is necessary. No fiction is involved. Do your homework.
<HR>
Hehe...I can see you're new here. chroot did his homework, and he still does. Go back and read his replies again. To 'assume' the ficticious forces of acceleration is not to 'guess' or make a conjecture about them, it is to apply them directly to the function
F=ma by the means of simple transformation.

He made a distinct point, clarifying why the forces are considered ficticious and that they must be dealt with discreetly.

Originally posted by NileQueen
What the heck are "fictitious forces"? F=ma is a basic law of science and it is universal. No assumption is necessary. No fiction is involved. Do your homework.

It is better to be silent and thought a fool than to speak up and prove it.

http://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&safe=off&q=fictitious+force

- Warren

Originally posted by NileQueen
If earth was the only thing in the universe would it even BE rotating?

I think so. If the Earth were rotating at 11 km/s where you’re at, you’d be weightless, having attained escape velocity. If you ran at 11 km/s in the opposite direction, you’d gain your maximum weight. So I see rotation as a partial orbit. If Earth was the only thing in the universe, you could tell if it was rotating by checking the escape velocity from the points of a triangle on the surface. If the escape velocity is constant, the Earth is not rotating. Alternatively you could use a Foucault pendulum. If these methods didn’t work when the Earth was the only thing in the universe, then a paradox would arise if you could still launch a rocket into orbit.

How did the earth start rotating in the first place? All the planets, and the sun rotate. Why is that?

Someone else could better answer these. I’d say it’s leftover energy from these bodies’ formation. Eventually the same hemisphere of the Earth will face the Sun always. The Earth’s rotation is continuously slowing.

Originally posted by NileQueen
How did the earth start rotating in the first place? All the planets, and the sun rotate. Why is that?
Conversation of angular momentum. A large gas cloud rotates very slowly -- as it collapses, it must rotate faster and faster.

When a gas cloud is just starting to collapse, it will always have some random net angular momentum -- even if it's just one more atom going one direction than the other. As it collapses, the rotation is "magnified."

- Warren

Okay I'll admit I was brash in making those comments, but I wouldn't have found out what fictitious forces were just sitting here behaving myself. I'll investigate and get back to you. Thanx.

NQ :)

That’s the spirit! Those who behave rarely make history.

chroot:Conversation of angular momentum. A large gas cloud rotates very slowly -- as it collapses, it must rotate faster and faster.
Alright I am going to blurt something out again in my foolish way. :D Don't you mean conservation of angular momentum? Or are the planets chatting? ;)

Originally posted by NileQueen
Don't you mean conservation of angular momentum?
D'oh! My fingers always do this.

- Warren

I guess you can provoke conversation with that law ;) So what bright spark decided to call those forces fictitious. One of the webpages had text expressing dismay at such a term :)

I always thought that 'fictitious forces' was a good name. The force appiled to solve the problem are fake and derived from knowledge of the rotation to make the problem easier.

I'm still reading...
these are good linx

http://id.mind.net/~zona/mstm/physics/mechanics/framesOfReference/nonInertialFrame.html

http://electron4.phys.utk.edu/141/sep29/September29.html

Does the sun wobble in its rotation? (earth ranges 22 - 25º over ~25,600 years)..it is more massive and so may not be pulled this way and that (very gradually) the way the earth is by sun, moon and planets

Yes I know the earth's rotation is slowing down. I believe it was fossil coral clox that revealed that?...

I think the term "fictitious force" is misleading. These forces are very real in the reference frames which experience them. I prefer to use the term "inertial force".