Suppose some way could be found obtain energy from the Earth’s rotation and use it to power civilization. How much energy could we leech from the Earth’s angular momentum before the effects would become noticeable?
With the atomic clocks that are now used to determine such things as how long a day is, it wouldn’t take long.
If you mean how long would it take the average person. I would think that if a day changed by as much as 5 minutes it be less than 20 years. We would notice that sunrise and sunset were out of wack.
Or that we had to keep setting our watches. 
And we are using the earth’s rotation for power, and slowing down in the process. Tidal power generation does exactly that. Don’t know it is enough to be measured.
http://www.iclei.org/efacts/tidal.htm
http://acre.murdoch.edu.au/ago/ocean/tidal.html
There’s a whole heck of a lot of energy in the angular momentum of the mass of the Earth. I don’t see how you might get at it, though.
It would be easier to tap the power of the heat of the Earth’s interior - just remove a cylinder of rock a mile wide and ten miles deep and let the yumminess pour forth. Actually that’s a bad idea. Increasing the earth’s atmospheric temperatur eand all.
Temperature difference, difference… Dig down deep and fill the hole with a good conductor of heat (diamond) and let it conduct heat up to the surface. You can make a large-scale generator of electricity where the cool atmosphere (or ocean or ice cap) meets the upflowing heat. Whatever kind of generator you like - but if the ability to produce large amounts of diamond has been discovered, then there will probbaly be a better large-scale way of generating electricity than with steam turbines.
Yeah, don’t mess with earth. Slow down the moon’s rotation–that way we’d get energy, plus we’d be able to see the dark side occassionnally.
Let’s assume we’ve hired a mad scientist who can convert the earth’s angular kinetic energy directly into electricity. According to my calculations, if civilization gives a power draw of P, and the earth has a moment of inertia I and a period T, and we only want to change the period by a small amount dT, then we could power civilization for an amount of time equal to:
t = 4 pi[sup]2[/sup] I dT / (T[sup]3[/sup] P)
Let’s say we don’t want the day to lengthen by more than dT = 1 second.
The moment of inertia of the Earth is 8.034 × 10[sup]37[/sup] kg m[sup]2[/sup].
The world energy consumption rate for 1995 was P = 316,000,000,000,000,000 BTU / year = 1.056 × 10[sup]13[/sup] W.
One year is T = 3.156 × 10[sup]7[/sup] s.
We could power civilization for 9553 s = 2 hours, 39 minutes. Not nearly as long as I would have guessed. And if we drew every last bit of spin from the earth, stopping it, we’d get enough power for 4776½ years. These numbers seem unastronomically low to me; did I screw up somewhere?
Maybe I am the one doing it wrong, but using your formula (which I just confirmed) and your numbers (which I haven’t), I arrive at t=5x10[sup]11[/sup] sec. Using all the kinetic energy gives you 2x10[sup]29[/sup] Joules, enough for 10[sup]8[/sup] years.
The kinetic energy of a rotating object is .5I[symbol]w[/symbol][sup]2[/sup], where I is the polar moment of inertia about its rotational axis, and [symbol]w[/symbol] is its angular velocity. Given I = 8.034 kg-m[sup]2[/sup] per Achernar’s cite, one can calculate the earth’s total angular kinetic energy, as well as the change in energy if it slowed down by a given amount.
The earth rotates about its axis once a sidereal day, or every 23:56:04. This is equal to 86164 seconds. The angular velocity [symbol]w[/symbol] = 2[symbol]p[/symbol]/86164, or 7.29212352 x 10[sup]-5[/sup] radians/sec.
Plugging these values back into the first equation yields 2.14 x 10[sup]29[/sup], or enough energy to power civilization (at 3.334 x 10[sup]20[/sup] J/year) for 641 million years.
Slowing down the rotation of the earth by one second per year would release 4.96 x 10[sup]24[/sup] J, or enough energy to supply our needs for nearly 15,000 years.
It’s late in the central time zone. Pretend you see a “x 10[sup]37[/sup]” in there.
Aha! Finally I see the error of my ways! And it was on the simplest number, too. T is one day, not one year. T = 86164 s, as per KeithT’s post. I also agree with the answer of 15,000 years.
Although, oddly enough, that’s the figure I get for slowing the earth’s rotation by one second per day, not one second per year…
Yeah, the rotation of the Earth (T) is one day, not one year. Multiply your answers by 365^3 and you get the same as scr4.
The earth does slow down because of lunar tidal drag, at the rate of a couple millisecond in a day per century. That energy is enough to raise the moon a couple centimeters every year.
Just don’t make the earth spin backwards; you know what will happen.
I guess we can answer the OP. It appears that we are using 7 times the energy that is being dissipated in the tides by tidal slowing. So, if 15% of our energy came from Telemark’s tidal generators, we’d be doubling that slowdown rate.
Since the length of day was defined as that of the mean day of the year 1900, and it’s been just over a century since then, the earth rotation takes about 2 milliseconds more–so we need a leap second about every 500 days, on average. Doubling that now, would mean, in a hundred more years, we’d be needing leap seconds every six months.
The problem with that answer is that you are assuming that if a whole bunch of new energy was available we wouldn’t start using a whole bunch more. 
[sup]We would.[/sup]
LOL. No, I think the real problem with that is that it would be hard to find a way to actually do it. I’m pretty sure [sup]we wouldn’t.[/sup]