Foucault Pendulum

[Derec]

If all the energy of earths rotation was suddenly absorbed by the earth itself, the first indicator would probably be the fact that the entire planet would be a molten ball of lava. I hate it when that happens!

No, it wouldn't. The temperature would go up, but by maybe ~70K or so, nowhere close to melting rock.
Calculation is left to the reader as an exercise.

 

[bilby]

If all the energy of earths rotation was suddenly absorbed by the earth itself, the first indicator would probably be the fact that the entire planet would be a molten ball of lava. I hate it when that happens!

No, it wouldn't. The temperature would go up, but by maybe ~70K or so, nowhere close to melting rock.
Calculation is left to the reader as an exercise.

The energy is irrelevant. The question is, where are you putting all the angular momentum?

Or don't we torque about that?

 

[Derec]

The energy is irrelevant. The question is, where are you putting all the angular momentum?

Great point! Moon maybe? It is already taking our angular momentum, albeit very slowly.

 

[Elixir]

The energy is irrelevant. The question is, where are you putting all the angular momentum?

Great point! Moon maybe? It is already taking our angular momentum, albeit very slowly.

Nope. Stopping the earth isn’t going to turn the moon into a molten blob, it would turn the earth into a semi- molten blob.

 

[Derec]

Nope. Stopping the earth isn’t going to turn the moon into a molten blob, it would turn the earth into a semi- molten blob.

I have already calculated that all the rotational kinetic energy of Earth's rotation would correspond to only ~70 K (or °C) increase in temperature of the Earth. Not enough to semi-melt rock. You can do the calculation yourself if you don't believe me.
But bilby made a great point about conservation of angular momentum. Where would you put that? What is your mechanism for stopping Earth's rotation?
That's why I brought up the Moon. The Moon has been doing this for billions of years via tidal forces. Earth's rotation is slowing down, and the Moon's orbital momentum is increasing along with its distance to Earth. A few billion years ago Earth's day was <20 h and the Moon was closer.

 

[steve_bank]

If you stopped the rotation of the Earth the energy has to show up as another form of energy, that is conservation.

Two balls collide with total KE = KE1 + KE2. After collision the KE total equals initial KE total minus loses in dformation of the balls, shows up as heat.

Attach a magic jet engine to the Earth to stop rotaton and I'd say the KE goes to heat.

As a rough approximation temperature rise would be by q = m*c*dT. Where q is energy in Joules, m is mass of Earth and c is an approximate specific heat of the Earth and dT change in temperature.

9.5: Rotational Kinetic Energy

The rotational kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy.

phys.libretexts.org

As the Earth has a period of about 23.93 hours, it has an angular velocity of 7.29×10−5 rad/s. The Earth has a moment of inertia, I = 8.04×1037 kg·m2. Therefore, it has a rotational kinetic energy of 2.138×10^29 J. The Rotating Earth: The earth's rotation is a prominent example of rotational kinetic energy.Jan 14, 2019

 

[bilby]

Nope. Stopping the earth isn’t going to turn the moon into a molten blob, it would turn the earth into a semi- molten blob.

I have already calculated that all the rotational kinetic energy of Earth's rotation would correspond to only ~70 K (or °C) increase in temperature of the Earth. Not enough to semi-melt rock. You can do the calculation yourself if you don't believe me.
But bilby made a great point about conservation of angular momentum. Where would you put that? What is your mechanism for stopping Earth's rotation?
That's why I brought up the Moon. The Moon has been doing this for billions of years via tidal forces. Earth's rotation is slowing down, and the Moon's orbital momentum is increasing along with its distance to Earth. A few billion years ago Earth's day was <20 h and the Moon was closer.

Unfortunately, the Moon is no longer available, having broken out of Earth orbit and left the solar system on September 13, 1999.

 

[Loren Pechtel]

If all the energy of earths rotation was suddenly absorbed by the earth itself, the first indicator would probably be the fact that the entire planet would be a molten ball of lava. I hate it when that happens!

No, it wouldn't. The temperature would go up, but by maybe ~70K or so, nowhere close to melting rock.
Calculation is left to the reader as an exercise.

One problem, though--it would show up unevenly. At the poles you would see no heating. At the equator you suddenly have 465 m/s being converted into heat--that's going to get very warm.

 

[bilby]

If all the energy of earths rotation was suddenly absorbed by the earth itself, the first indicator would probably be the fact that the entire planet would be a molten ball of lava. I hate it when that happens!

No, it wouldn't. The temperature would go up, but by maybe ~70K or so, nowhere close to melting rock.
Calculation is left to the reader as an exercise.

One problem, though--it would show up unevenly. At the poles you would see no heating. At the equator you suddenly have 465 m/s being converted into heat--that's going to get very warm.

Still only 100kJ per kg of rock though. The temperature is going up maybe 125K; That's more than enough to fry an egg, and likely gets you close to 150°C, so hot enough to boil the ocean too, but nowhere near enough to melt rock.

 

[Loren Pechtel]

If all the energy of earths rotation was suddenly absorbed by the earth itself, the first indicator would probably be the fact that the entire planet would be a molten ball of lava. I hate it when that happens!

No, it wouldn't. The temperature would go up, but by maybe ~70K or so, nowhere close to melting rock.
Calculation is left to the reader as an exercise.

One problem, though--it would show up unevenly. At the poles you would see no heating. At the equator you suddenly have 465 m/s being converted into heat--that's going to get very warm.

Still only 100kJ per kg of rock though. The temperature is going up maybe 125K; That's more than enough to fry an egg, and likely gets you close to 150°C, so hot enough to boil the ocean too, but nowhere near enough to melt rock.

Huh? He's saying an average of 70K--but there's a lot more mass closer to the rotational axis than farther from it, how can you have less than twice the energy on the equator?? (I'm not saying who is right, just that I see no way both of you can be.)

 

[bilby]

If all the energy of earths rotation was suddenly absorbed by the earth itself, the first indicator would probably be the fact that the entire planet would be a molten ball of lava. I hate it when that happens!

No, it wouldn't. The temperature would go up, but by maybe ~70K or so, nowhere close to melting rock.
Calculation is left to the reader as an exercise.

One problem, though--it would show up unevenly. At the poles you would see no heating. At the equator you suddenly have 465 m/s being converted into heat--that's going to get very warm.

Still only 100kJ per kg of rock though. The temperature is going up maybe 125K; That's more than enough to fry an egg, and likely gets you close to 150°C, so hot enough to boil the ocean too, but nowhere near enough to melt rock.

Huh? He's saying an average of 70K--but there's a lot more mass closer to the rotational axis than farther from it, how can you have less than twice the energy on the equator?? (I'm not saying who is right, just that I see no way both of you can be.)

Both figures are in the same order of magnitude; twice 70 isn't far from 125.

I suspect the difference is in our selection of materials - I just used the heat capacity figure for granite in my back of the envelope calculations, because, when discussing the fastest moving parts of the Earth, it's equatorial surface rocks you're heating.

Likely Derec used a more appropriate figure for the actual materials that make up the planet, which contains a lot of iron, which would make sense if calculating a whole planet average figure, rather than a figure for the surface rock at the equator.

I figured that more accurate calculations were pretty pointless; For a crude estimate, I just took a bunch of things for granite.

 

[steve_bank]

The heat would not come from the mass of the Earth as it slows down.

A magic super powerful space ship attahces to the Earth with a very long cable away form the panet.

The ship pulls against the Earth's rotation. The loss in KE of the Earth shows up in the ship. The ship heats up.

Thee engine in a car is turned off and is coasting. A car in front uses its brakes to slow the coasting car down. The coasting car does not heat up, the stopping car does.

If there is a slowing mechanism on the Earth then the mechanism would be the hot spot. Some energy escapes the Earth as radiation, the rest progates through the Earth based on thermal resistance .

Or so I think. Good question for whoever started it going.

 

[bilby]

A magic super powerful space ship attahces to the Earth with a very long cable away form the panet.

The ship pulls against the Earth's rotation. The loss in KE of the Earth shows up in the ship. The ship heats up.

Not appreciably. Mostly the energy is going to end up as kinetic energy of the ship, and/or whatever reaction mass it's rockets expel.