Space elevator wondering about torque

[fahraynk]

Say you have an elevator that reaches space. I have 2 questions :
1) say a space rock hits the top of the elevator... that would create a torque = force * distance on the ground... Wouldn't it instantly snap from any light force or space junk hitting the top of the elevator? Would the station have to instantly compensate for something like this?

If this is true, any compensating force would have to act really fast right? Because if the force is countered so that it lasts for only a millisecond maybe it won't be long enough to make the material break (maybe it needs time to pass the materials elasticity region or something). Or would it create some kind of force wave going back and forth through the tower if the force only acts for a half a second?

2) Someone was asking on facebook about the Earth slowing down like when an ice skater spreads out their arms while spinning. I think the moment of the inertia of Earth would be so great that the change from a space elevator would not have any effect. But in theory it should have SOME minute effect... So my question is... if you remove the space elevator, would momentum be conserved and that minute amount of rotational velocity the elevator might remove from the Earth would be instantly retrieved, so that the Earth's rotational speed goes back to the pre elevator speed?

 

[sophiecentaur]

Apart from the strength issue, there is the problem that a space elevator tether would be at risk of collision from every non-geosynchronous satellite, eventually.
The angular momentum situation would depend on the construction method. If it starts with a mass, placed in geosynchronous orbit then the angular momentum of the mass would have been increased by the rockets placing it in orbit. If it's made by building a tower from ground up, the angular momentum would be shared with the Earth so you would get a theoretical slowing down - but, do the sums - not detectable.

 

[jbriggs444]

Say you have an elevator that reaches space. I have 2 questions :
1) say a space rock hits the top of the elevator... that would create a torque = force * distance on the ground... Wouldn't it instantly snap from any light force or space junk hitting the top of the elevator? Would the station have to instantly compensate for something like this?

Large angular momentum, sure. But nothing is deflecting very much, so nothing is going to break because of the deflection.

Or would it create some kind of force wave going back and forth through the tower if the force only acts for a half a second?

Yes, a deflection at the top would cause a wave to propagate down the elevator. Exactly like a wave on a string.

2) Someone was asking on facebook about the Earth slowing down like when an ice skater spreads out their arms while spinning. I think the moment of the inertia of Earth would be so great that the change from a space elevator would not have any effect. But in theory it should have SOME minute effect... So my question is... if you remove the space elevator, would momentum be conserved and that minute amount of rotational velocity the elevator might remove from the Earth would be instantly retrieved, so that the Earth's rotational speed goes back to the pre elevator speed?

You are right. It would, in theory, have a minute effect on the rotation speed of the Earth, too small to be measured.

When you remove the elevator, are you severing the tie and allowing it to be ejected into space? If is it ejected then the angular rotation of the Earth will remain at its reduced rate. If it is reeled back in then the angular rotation rate of the Earth will return to normal, like a skater pulling her arms back in.