Perfect spheres and spin

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Perfect spheres and spin

Postby vivian maxine on January 25th, 2016, 9:00 am 

If our planets or asteroids, etc., were perfect spheres, would they spin faster?
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Re: Perfect spheres and spin

Postby Natural ChemE on January 25th, 2016, 12:48 pm 

vivian maxine,

Depends on what other variables you hold constant when transforming the planets into perfect spheres.

Spinning things tend to be wider at their equator due to the spinning. By analogy, it's kinda like you're in a swivel chair or bar stool, going around in circles with your legs out. If you suddenly pull your legs in toward the axis of rotation, you'll spin faster due to the conservation of angular momentum.

So, if you conserve angular momentum when you make the planets into perfect spheres, they should spin faster. Larger planets will probably only speed up a bit (in relative terms) because they're pretty close to spheres already, but small asteroids might speed up by a large factor.
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Re: Perfect spheres and spin

Postby vivian maxine on January 25th, 2016, 1:16 pm 

Natural ChemE » January 25th, 2016, 11:48 am wrote:vivian maxine,

Depends on what other variables you hold constant when transforming the planets into perfect spheres.

Spinning things tend to be wider at their equator due to the spinning. By analogy, it's kinda like you're in a swivel chair or bar stool, going around in circles with your legs out. If you suddenly pull your legs in toward the axis of rotation, you'll spin faster due to the conservation of angular momentum.

So, if you conserve angular momentum when you make the planets into perfect spheres, they should spin faster. Larger planets will probably only speed up a bit (in relative terms) because they're pretty close to spheres already, but small asteroids might speed up by a large factor.



That's what I meant - a perfect sphere would have fewer variables in pressure which would allow it to spin faster. I'm not sure what that pressure is. Near the ground, it would be moving air but that doesn't apply to planets. If there is any kind of pressure against the planets that helps keep them spinning (my assumption), wouldn't it be stronger in some spots than in others on an amorphous (imperfectly-shaped) sphere?

Thank you for the explanation.
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Re: The Shape of Spin

Postby Faradave on January 25th, 2016, 3:10 pm 

I don't think you have to worry much about pressure here. It's distribution of mass that counts. The closer the mass is to the axis of rotation the faster it will spin for a given angular momentum. For example, a body shaped like rod will spin faster about the long axis than if it was a sphere.

Planetary bodies that are predominantly fluid (including magma), will bulge at the equator if spinning. Spinning solids will also deform but to a much lower degree. A perfect sphere is most likely with a large fluid body that lacks spin and is not accelerating (i.e. is far from other gravitation sources) in any other way.
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Re: The Shape of Spin

Postby vivian maxine on January 25th, 2016, 3:55 pm 

Faradave » January 25th, 2016, 2:10 pm wrote:I don't think you have to worry much about pressure here. It's distribution of mass that counts. The closer the mass is to the axis of rotation the faster it will spin for a given angular momentum. For example, a body shaped like rod will spin faster about the long axis than if it was a sphere.

Planetary bodies that are predominantly fluid (including magma), will bulge at the equator if spinning. Spinning solids will also deform but to a much lower degree. A perfect sphere is most likely with a large fluid body that lacks spin and is not accelerating (i.e. is far from other gravitation sources) in any other way.


OK. Got that. But where the sphere is concerned, will a perfect sphere (all points equidistant from the center) spin faster than an amorphous (crooked/no real center from all points)? Seems that would be so as, in the latter case, part of it is closer to what should be the center than other parts.

I was thinking it would be more likely to be true with a rocky planet but that was when I was thinking pressure. If it is a matter of equidistance from a center, maybe it would more likely apply to gaseous planets? Rocky planets have their bulges all around.

Rods are faster, though. I didn't realize that. Thanks.
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Re: Perfect spheres and spin

Postby Faradave on January 25th, 2016, 8:36 pm 

vivian maxine wrote:will a perfect sphere (all points equidistant from the center) spin faster than [a lumpy object]

It depends on the average distance of the mass from the spin axis. The closer the average mass is to that axis, the faster it will spin for a constant angular momentum.

Image

This lady is nicely lumpy, yet puts herself into a rod-like configuration, rather than a ball, to produce the greatest angular velocity. When she wants to slow down, as NCE alluded, she'll put her arms out.

So no matter how lumpy, with average mass is closer to the axis of rotation, an object will spin faster, even faster than a ball. (Technically, a "sphere" is the surface enclosing a "ball" so a hollow "spherical" object will spin slower than a ball of the same mass, since its average mass is further from the axis of rotation.)
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Re: Perfect spheres and spin

Postby Dave_Oblad on January 25th, 2016, 10:09 pm 

Hi Viv,

Vivian wrote:If our planets or asteroids, etc., were perfect spheres, would they spin faster?

I'm confused by the word "faster". So.. faster implies an external force has to change it from what it was previously.

In a Vacuum, the speed something is rotating at will always be the rotation speed.. unless acted upon by an external body or the re-distribution of its mass.

Yes.. changing somethings shape can change its speed of rotation and make it Faster or Slower. So, best guess as to what you are asking is.. Yes, if you took the bulge out of a Planet/Star equator and re-distributed said mass.. it would spin faster.. but that faster spin would attempt to re-distribute said mass and slow down to some ideal speed again.

For example, the melting of our Polar Caps is probably making our days a tiny bit longer. If we could reverse global warming and rebuilt our Polar Caps, our days would become a tiny bit shorter.

Regards,
Dave :^)
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Re: Perfect spheres and spin

Postby vivian maxine on January 26th, 2016, 8:06 am 

I surrender. There is something wrong in how I am asking my question but I don't know what it is. So, I give up.
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Re: 39 seconds more

Postby Faradave on January 26th, 2016, 11:58 am 

Viv,

Check out this video of a ring vs. a disk (analogous to sphere vs. ball).



With narration at 3 min, this video explains the first.



This video has an equation but it's well explained in 3 min. Note that to simulate lumpiness (asymmetry), she often sticks just one leg out to slow down. The average distance form the axis of rotation is more important than symmetrical distribution. Greater average radius means slower spin for a given spin energy.



Hope that helps.
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