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Why do we rotate along with the earth's rotation?

by Astaroth
Tags: earth, rotate, rotation
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asdofindia
#91
Apr3-11, 09:35 PM
P: 29
Quote Quote by cepheid View Post
You do NOT need to invoke friction at any point in history (not even going back to Earth's formation) to understand why everything that makes up part of the Earth is rotating. Only conservation of angular momentum need be applied.
I thought conservation of angular momentum was applicable only to a rigid body rotating on its own axis. In that case we'd have to be glued to earth's surface from time immemorial.

(But that's what the gravitational force and friction do. Gluing us to the surface)

So, the answer is a complex interplay of conservative and non-conservative forces, and conservation of motion.
Drakkith
#92
Apr4-11, 02:02 AM
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I agree with asdofindia. It is a result of several forces over a long period of time. But in the short term, we don't need friction to keep us rotating with the earth.
asdofindia
#93
Apr4-11, 02:19 AM
P: 29
Imagine a magnetic sphere. Rotating.
Imagine a sticky man on it with iron legs. Let's say he already has acquired the velocity of the point right under his legs.
At every point, the man's velocity wants him to go tangential to the surface, to be thrown away from the sphere.
But the magnetic force pulls him onto the sphere.
(Centrifugal and centripetal forces)
Agreed till now?
The centrifugal force and centripetal forces are exactly opposite and cancel each other. But they've got no component along the surface of the sphere!!
(So there's got to be friction???!!!???!!!)
I don't think I've understood my answer.
Drakkith
#94
Apr4-11, 02:20 AM
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The centrifugal force and centripetal forces are exactly opposite and cancel each other. But they've got no component along the surface of the sphere!!
What do you mean by this?
asdofindia
#95
Apr4-11, 02:26 AM
P: 29
See, if we draw a free body diagram. We'd draw an arrow from the man to the centre, calling it centripetal force. And another opposite to it calling it centrifugal force, right?
I thought they'd cancel, but I don't think I've clearly finished that thought process, I made a quick reply...

And of course they wouldn't have any component tangential to the surface.

But a body already moving with a velocity tangential do not need a force to keep it moving along the tangent.
But that's along the tangent...

Oh... I think I'm confused. Let me think for a while...
Drakkith
#96
Apr4-11, 02:32 AM
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The force holding the man to your sphere is the magnetic force between his legs and the sphere. This force is greater than the upward force trying to push him away. If it wasn't any small simply movement by the man would send him moving upwards and away.

Because of this, the man is constantly being pulled down towards the sphere while also moving...tangently??...through space around the sphere. The magnetic force on him is similar to the gravitational force on a satellite in orbit. The satellite is constantly falling towards the earth, but also moving, resulting in an orbit.
asdofindia
#97
Apr4-11, 02:36 AM
P: 29
That makes me wonder whether or not to subtract mv2/r from GMm/r2 when calculating the weight of a body

Edit:http://en.wikipedia.org/wiki/Centrif...tious%29#Earth
Appears like there are effects due to centrifugal force
Drakkith
#98
Apr4-11, 02:53 AM
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There are most definately effects due to the centrifigal force. They are usually so small as to be irrevelent in day to day stuff. However, for space launches we do calculate that effect as well as the velocity of the earths rotation from the launch site in order to put something into orbit correctly.
asdofindia
#99
Apr4-11, 03:04 AM
P: 29
Centripetal force, Fg=GMm/r2
Centrifugal force, Fr=mv2/r
So, when v is > vmax where vmax> [tex]\sqrt{GM/r}[/tex] we do fly away!! If it's [tex]\sqrt{2}[/tex] times the vmax in the above equation, it'd escape earth's gravity too (because that'd be 11.2 km/s)
If v/vmax is between 1 and [tex]\sqrt{2}[/tex], it'd fly away and fall down back.
(But luckily on earth, v is approximately 1/17 times vmax)
That's why we're not flying away from earth.

Now, let me do something I've never done before.

Since the centrifugal force on earth is cancelled out by the gravity (289 times stronger), we can safely assume the body to be at rest with respect to the reference frame of earth. (I don't know if that's right, because as I said, I've never done this before) (There'd be no longer any effects that'd be observed due to rotational motion of earth with respect to the space around it)
So, since earth and the body are both at rest (in that inertial frame) there wouldn't be the need of any frictional force.

We have to view this in the inertial frame of earth.

(I have understood my point)
Lsos
#100
Apr4-11, 07:46 AM
P: 777
Quote Quote by singh94 View Post
i mean a person who is in space. if everything was not moving(not at respect to eachother but in actual) then he would be at rest with respect to them. now do u get it
I'm not sure what you are asking, but when you are in orbit in space then we can confidently say that you are NOT rotating with the earth. You are moving much, much faster than the earth is spinning.

Now what happens when you re-enter the atmosphere? The atmosphere WILL slow you the fuk back down to it's own speed, and it will use extreme force to do so. The force is so great in fact, that whatever is re-entering must use some kind of heat shield, otherwise it will burn up with a brightness of the sun.

So you see what happens whenever something is not rotating with the earth. The earth WILL slow or speed it up to match its own rotation, and violently so if need be. If you don't believe me go jump out of a moving car, and you'll see first hand how it feels when something is NOT rotating with the earth.
JaredJames
#101
Apr4-11, 08:25 AM
P: 3,387
asdofindia centripetal force is not gravity. Your equation above defines gravity not centripetal force.

Note, your equation is virtually constant wherever you are on the planet, which is gravity, but the centripetal force is almost zero at the poles and maximum at the equator.
asdofindia
#102
Apr4-11, 08:28 AM
P: 29
Quote Quote by jarednjames View Post
asdofindia centripetal force is not gravity. Your equation above defines gravity not centripetal force.

At the poles there is virtually no centrifugal forces compared to at the equator.
So the centripetal force is......?
JaredJames
#103
Apr4-11, 08:31 AM
P: 3,387
Quote Quote by asdofindia View Post
So the centripetal force is......?
Centripetal force occurs due to a body moving on a curved path.

Gravity occurs simply because a body has mass.

We have both on earth, one is down to the mass, the other the rotation.

Gravity, aside from the ellipsoid shape of the earth is relatively constant all over the planet.

Centripetal force is at its maximum at the equator and tends to zero towards the poles.
asdofindia
#104
Apr4-11, 08:50 AM
P: 29
Quote Quote by jarednjames View Post
Centripetal force is at its maximum at the equator and tends to zero towards the poles.
yeah, i was talking at the equator.
JaredJames
#105
Apr4-11, 09:15 AM
P: 3,387
Quote Quote by asdofindia View Post
yeah, i was talking at the equator.
Doesn't matter.

You are describing gravity as centripetal force which is incorrect.
asdofindia
#106
Apr4-11, 09:17 AM
P: 29
And I'm also asking if gravity is not centripetal force, what's keeping us glued to earth on the equator where we ARE doing a curved motion. You saying friction?
JaredJames
#107
Apr4-11, 09:20 AM
P: 3,387
Quote Quote by asdofindia View Post
And I'm also asking if gravity is not centripetal force, what's keeping us glued to earth on the equator where we ARE doing a curved motion. You saying friction?
GRAVITY!

Gravitational force is far greater than the opposing force trying to "fling us off" at the equator.

But this does not mean gravity is centripetal force.

Gravity: http://en.wikipedia.org/wiki/Gravitation

Centripetal Force: http://en.wikipedia.org/wiki/Centripetal_force
D H
#108
Apr4-11, 10:02 AM
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Centripetal force is a bit of a misnomer. A better term is centripetal acceleration. From the perspective of a non-rotating observer, a person standing still on the surface of the Earth undergoes uniform circular motion. From a kinematics perspective, there is a centripetal acceleration toward the center of rotation (which in general is not the center of the Earth) associated with this observed uniform circular motion.

Multiplying this observed centripetal acceleration by mass yields the net force on the person. This net force cannot be attributed to any one force because multiple real forces act on the person: gravitation, the normal force, buoyancy, etc. Note that centrifugal force is not one of these. Centrifugal force is not a real force. It simply does not exist from the perspective of our non-rotating observer.

What about a non-inertial point of view, for example, a frame rotating with the rotating Earth? From the perspective, the person standing still on the surface of the Earth is (duh) standing still. To give the appearance that Newton's first and second laws still apply, the net apparent force acting on the person must be zero. We're looking at things from the perspective of a rotating frame, so there is a centrifugal force at play here. This in turn means there must be some other forces whose sum is exactly counter to this centrifugal force.

Not surprisingly, this net non-centrifugal force calculated by the rotating observer is exactly the same as the net force calculated by the non-rotating observer.


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