Can Dark Matter and Black Holes be Associated in Earth's Rotation?

[thinkies]

......so,what makes Earth rotate...I believe I'm still in my *discovery*phase(normal for a 15 yrs old..)...sry if this is a newbish question...

I though looking on the internet..but so lazy and beside i will prob. not understand with they complicated terms and stuff they'll use to explain...o.0

also,i dun know if this makes sense or not,but can we assosiate dark matters with black holes...in someway,such as...dark matters can not be be seen and if I am not wrong they don't even show any signs of energy(if they had,im sure they would produce some sort of gamma rays or w/e,=.=right?)..whereas black holes,we know they exist,yet...still many mysterious facts remain...

? so confused...o.0
hmmm any books recommendation...I was wondering to take some books and learn basics(very very very basic stuff...)about quantum mechanic(are they even useful in astrophysics?)..

Thx:D

 

[thinkies]

...

hmmmm......
so..

 

[Woozie]

When the solar system was formed, the matter had angular momentum. When the matter clumped together, the angular momentum from the individual pieces of matter had to be conserved, so things formed from this matter (like planets and even the sun itself) rotates.

 

[DaveC426913]

Dark matter was hypothized as an explanation of why we see galaxies holding together while rotating too fast to do so. The only thing that seems to explain it is if the galaxies have more mass than we see. Not sure if that helps.

 

[thinkies]

woha...i dun think that i got wut you guys really are sayin...umm..then how come its still rotating...i mean,there's something...or else ..it wouldn't be rotating since all those years that passed...right? o.0btw,im not even sure if i get this 'angular momentum'...and why did the matters had angular momentum when the solar system formed?

and...hmmmmmm exactly how did we find out the existence of dark matters...?

 

[OmCheeto]

woha...i dun think that i got wut you guys really are sayin...umm..then how come its still rotating...i mean,there's something...or else ..it wouldn't be rotating since all those years that passed...right? o.0btw,im not even sure if i get this 'angular momentum'...and why did the matters had angular momentum when the solar system formed?

Well, it's like a big ol' gyroscope in a vacuum.
Once you get it going, there's nothing to slow it down. (except for the moon of course)
You really need to do the math:

earth mass = 6e24kg
earth radius = 6.371km
rotational speed = 24 hours

um... I'm not near my calculus book at the moment ...

and the web seems to be a bit light on spherical gyro's today,

and...hmmmmmm exactly how did we find out the existence of dark matters...?

That's still way out there so I'll wait till morning to attempt an answer.

 

[DaveC426913]

I think we would be a lot more willing to discuss this with you if you made an attempt to write intelligibly. It sort of feels like we're entertainnig a drunk.



In our everyday world, we are used to seeing spinning objects gradually slow down and stop - like a spinning top running down. But this is actually the exception to the rule. Newton's first law states that 'things in motion will tend to stay in motion unelss acted upon by an outside force'.

Things slowing to a stop happens usually because of friction - in the case of the top, friction with the table it's on and the air. If the top were set spinning out in space, it would spin forever.

So it is with the Earth.

All that being said, the Earth is actually slowing down; it's just taking billions of years to do so. If you notice, the Moon has slowed to a stop (with respect to Earth at least)

 

[OmCheeto]

I think we would be a lot more willing to discuss this with you if you made an attempt to write intelligibly. It sort of feels like we're entertainnig a drunk.



In our everyday world, we are used to seeing spinning objects gradually slow down and stop - like a spinning top running down. But this is actually the exception to the rule. Newton's first law states that 'things in motion will tend to stay in motion unelss acted upon by an outside force'.

Things slowing to a stop happens usually because of friction - in the case of the top, friction with the table it's on and the air. If the top were set spinning out in space, it would spin forever.

So it is with the Earth.

All that being said, the Earth is actually slowing down; it's just taking billions of years to do so. If you notice, the Moon has slowed to a stop (with respect to Earth at least)

I swear to god I just said all that a minute ago...
in different words of course.

 

[DaveC426913]

I swear to god I just said all that a minute ago...
in different words of course.

Yes, you just beat me to the post.

 

[OmCheeto]

Yes, you just beat me to the post.

so do you know where to find spherical gyroscopic equations outside of my old textbooks?
It's a question that's been going around for a day or two.

 

[DaveC426913]

so do you know where to find spherical gyroscopic equations outside of my old textbooks?
It's a question that's been going around for a day or two.

Uh, you got me. :shy:

Formally, I only have a high school level of ecucation in math - I barely passed Calculus. Thirty five years of reading has alloowed me to understand much of physics, but I don't really have the skills to do the formulae. Pity.

 

[Quincy]

o.0btw,im not even sure if i get this 'angular momentum'

You know if you spin on a... spinning chair or w/e with your arms/legs out, and then you turn your arms/legs in, the chair spins faster; that's angular momentum.

All that being said, the Earth is actually slowing down; it's just taking billions of years to do so. If you notice, the Moon has slowed to a stop (with respect to Earth at least)

Isn't that because it's tidally locked to Earth?

 

[LURCH]

Isn't that because it's tidally locked to Earth?

Yes, exactly. And, in the same way, the Earth is becoming tightly locked to the moon. This year takes 24 hours to complete one revolution, the moon orbits and much slower pace, taking 28 days to complete one orbit. Because of this, the gravitational attraction between the Earth in the moon is causing the moon to act like a break and slow the Earth's rotation, while simultaneously speeding up the moon's orbit. Given enough time, these two would eventually become synchronous, and the moon would occupy one spot in the sky always, without moving.

 

[thinkies]

well...let see if i really get it.
Basically,the Earth rotation begun when this solar system formed and it had this angular momentum.

It it is still rotating becuz of some Newton law,since there is no force in space,there's nothing to stop it.right? o.0...im very very slow at understanding :P

However,there is something i am not understanding.How canthe moon be affecting Earth rotation exactly...?

 

[Quincy]

well...let see if i really get it.
Basically,the Earth rotation begun when this solar system formed and it had this angular momentum.

It it is still rotating becuz of some Newton law,since there is no force in space,there's nothing to stop it.right? o.0...im very very slow at understanding :P

However,there is something i am not understanding.How canthe moon be affecting Earth rotation exactly...?

If you spin a top on Earth, it's eventually going to stop because of Earth's gravity right? Well, the rotation of the Earth is eventually going to stop because of the Moon's gravity.

 

[D H]

so do you know where to find spherical gyroscopic equations outside of my old textbooks?

Newton's second law of motion, \mathbf F=d\mathbf p/dt, is \mathbf \tau = d\mathbf L/dt, where \mathbf \tau is the total external torque and \mathbf L is the angular momentum expressed in inertial coordinates. The linear momentum of some body is given by \mathbf p = m\mathbf v. Similarly, the angular momentum of some rigid body is given by \mathbf L = \mathbf I\mathbf \omega. There is a complication with this latter expression. We typically represent the inertia tensor \mathbf I and the angular velocity \mathbf \omega in rotating coordinates rather than inertial coordinates. In a coordinate frame rotating with the body in question, the inertia tensor for a rigid, constant mass body is constant. This is not the case for the inertia tensor expressed in inertial coordinates.

Any decent junior-level (college) classical dynamics text will cover the relationship between derivatives of vector quantities in rotating and nonrotating frames:
\frac {d\mathbf q}{dt_{\text{fixed}}} = \frac {d\mathbf q}{dt_{\text{rot}}} + \mathbf \omega \times \mathbf q
where \mathbf q is any vector quantity. Some call this the transport theorem (not to be confused with the Reynold's transport theorem), some (e.g., Marion, Classical Dynamics) don't bother to give this relationship a name. (Marion does a lousy job proving it, BTW). Apply this relationship to the angular momentum vector:
\mathbf \tau = \frac {d\mathbf L}{dt_{\text{fixed}}} = \frac {d\mathbf L}{dt_{\text{rot}}} + \mathbf \omega \times \mathbf L = \frac {d}{dt}(\mathbf I \mathbf \omega) + \mathbf \omega \times (\mathbf I \mathbf \omega)
If the inertia tensor is constant in the rotating frame (and it is for an ideal rigid body), the inertia tensor comes out of the derivative. Solving for the time derivative of the body rate,
\mathbf I\dot{\mathbf\omega} =\mathbf \tau - \mathbf \omega \times (\mathbf I \mathbf \omega)

These are "[URL equations[/URL], just written a lot more compactly than usual.

 

[DaveC426913]

However,there is something i am not understanding.How canthe moon be affecting Earth rotation exactly...?

If the Earth were prefectly circular and perfectly rigid, it could not.

But the Moon causes lots of tiny forces of the Earth: it pulls on mountains and it sloshes water around. The net effect is friction - and a slowing of the Earth's rotation.

Think about this: You turn off a ceiling fan (so that its spinning freely with no force or friction) and want to bring it to a stop quickly. It's much faster to bring it to a stop by grabbing its blades than by grabbing its smooth, circular body. Think of the blades like the mountains and oceans of Earth.

 

[D H]

If you spin a top on Earth, it's eventually going to stop because of Earth's gravity right?

No. It will eventually stop because of friction. Friction between the end of the top and the surface on which it is resting exerts a torque on the top. Gravity itself does not exert a torque. All that gravity does is hold the top on the surface of the Earth. If you spun a perfectly rigid top in space it would spin forever.

The reason the Earth is slowing down is because of friction. The moon's gravity is a bit weaker on the side of the Earth away from the Moon than the side of the Earth facing the Moon. The tides result from this gradient in the gravitational acceleration. Friction between the rising and falling tides and the more-or-less solid Earth are what are slowing the Earth's rotation rate down.

EDIT: Dave C beat me do it. Dang.

 

[thinkies]

If you spin a top on Earth, it's eventually going to stop because of Earth's gravity right? Well, the rotation of the Earth is eventually going to stop because of the Moon's gravity.

=.=,earth's gravity is way more stronger then the moon...o.0,how can this be even possible...

 

[thinkies]

oh...i think I am getting this...but since this process may take million of yrs,in distant future,will there be a day/night concept...?(since it'll eventually slow down its rotating,as mentioned by some of you..)

also,for planets that do not have any natural satellite,will they keep rotating..for ever?

 

[thinkies]

also,this may be irrelevant wid this thread...but let's say we were to test a nuclear bomb on the moon...wut would be the consequence if it explodes on the moon o.0?is it even possible testing there? >.<

 

[DaveC426913]

oh...i think I am getting this...but since this process may take million of yrs,in distant future,will there be a day/night concept...?(since it'll eventually slow down its rotating,as mentioned by some of you..)

Certainly. Earth's prehistoric past had a much shorter day/night cycle. Shoot, I can't remember - was it as short as ten hours?

also,for planets that do not have any natural satellite,will they keep rotating..for ever?

All planets are in the gravitational grip of other planets and of the sun.

also,this may be irrelevant wid this thread...but let's say we were to test a nuclear bomb on the moon...wut would be the consequence if it explodes on the moon o.0?is it even possible testing there? >.<

Yes, this could be done. (But we wouldn't learn a lot, so there's little point.)

 

[D H]

also,for planets that do not have any natural satellite,will they keep rotating..for ever?

All planets are in the gravitational grip of other planets and of the sun.

That is true, Dave, but the time for a body orbiting about another body to be tidally lock to that second body is proportional to the sixth power of the radial distance between the two objects. The Sun will blow up to a red giant and fade to a white dwarf long before the Sun tidally locks the Earth. For the outer planets, it just won't happen.

 

[Sourabh N]

Well, I remember searching the same question(Rotation of Earth) on net, and I found that its due to the nuclear reactions going on inside earth.(Sorry, but i don't have the link to page now)

 

[Sourabh N]

Well, I remember searching the same question(Rotation of Earth) on net, and I found that its due to the nuclear reactions going on inside earth.(Sorry, but i don't have the link to page now)

 

[D H]

Well, I remember searching the same question(Rotation of Earth) on net, and I found that its due to the nuclear reactions going on inside earth.

You either misread or you read some woo-woo pyschoceramic claptrap garbage (and if you ask again, I'll tell you what I really think ).

The Earth is rotating because (a) the Earth was rotating when it was first formed, (b) angular momentum is a conserved quantity, and (c) the external torques on the Earth (i.e., tides caused by the Moon) are not large enough to have stopped the Earth's rotation.

Anything happening in the interior of the Earth does not qualify as an external torque.

 

[thinkies]

hmm...since the sun rotates too,if there was a greater attraction(more powerful then the sun)would it slow it down too...>.< or this would lead into some different scenarios...?

 

[thinkies]

bump...

 

[OmCheeto]

also,this may be irrelevant wid this thread...but let's say we were to test a nuclear bomb on the moon...wut would be the consequence if it explodes on the moon o.0?is it even possible testing there? >.<

Sorry I'm late.
This has nothing to do with nuclear bombs on the moon but does describe why the Earth keeps spinning, in a slightly more illustrative fashion.

The following assumes we could direct the energy from a nuclear blast to slow the rotation of the earth:

(energy is in Joules)

6.30E+13 energy from the Hiroshima bomb (ref 1)
2.57E+29 energy due to the Earth's rotation (ref 2)
4E+15 number of Hiroshima bombs equivalent to the Earth's rotational energy
1,440 number of minutes in a day (we're going to set off one bomb every minute)
2.83289E+12 number of day we need to explode the bombs
365.24 number of days in a year
7,756,249,086 number of years to stop the rotation of the earth.

That's 7.76 billion years setting off a nuclear bomb every 60 seconds.

So you see, there is a lot of energy stored in our planet due to it's rotation.

On a side note, I also ran across an interesting article about some spherical gyroscopes in orbit around our planet:

http://science.nasa.gov/headlines/y2004/26apr_gpbtech.htm
A Pocket of Near-Perfection
Now orbiting Earth, Gravity Probe B is a technologicaltour de force.
In this pristine, high-vacuum environment, the spherical gyroscope could spin at its operating speed of 10,000 rpm for 1,000 years without slowing by more than 1 percent.

And they are only an inch and a half across.

references
(1) http://www.carnicom.com/time3.htm kinetic energy of the rotation of the earth
(2) http://en.wikipedia.org/wiki/Megaton energy of the Hiroshima bomb

 

[thinkies]

hey,omcheeto,umm i know this will be a stupid question but let's say we were to explode a nuclear bomb on Earth's core...will it lead to some bad consequence?and what kind of consequence..?