Thread: How much rotational energy does the Earth have?

Like if you could harness all the energy of the Earth's rotation until it stopped spinning. How much energy would you have? Is there a formula for figuring this out? Using mass and rotation speed or something?

I know, but I'm not telling.

For translational kinetic energy the formula is E = 0.5*m*v^2 where m is the mass (inertia) and v is the velocity.
For rotational energy the formula is E = 0.5*I*(omega)^2 where I is the moment of inertia and omega is the angular velocity in radians per second.

Wikipedia has the following info:
As an example, let us calculate the rotational kinetic energy of the Earth. 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 = 8.04×10^37 kg·m^2. Therefore, it has a rotational kinetic energy of 2.138×10^29 J.

For a solid sphere of radius R and mass m (uniformly distributed, ie constant density) the moment of inertia is I = 0.4*m*R^2

you would lose energy, because it would take energy (the capacity to do work, which is force times distance) to stop the earth from spinning. if the earth just spun into something and stopped dead, and sent another thing flying (assuming you don't count heat generated by the friction) sort of like those clacking balls that transit their energy through the center balls to the ones at the edge, then the energy received would be equal to the earth's current kinetic (rotational) energy. that can be found by (1/2 mass) times (velocity squared).

the mass of the earth is 5.9722 * 10^24 kg, and it's rotational velocity is 1,674.4 km/h or 60,278,400,000 meter/sec. one joule is 1 kg * meter^2 / sec^2. so if you half the mass (2.9861 * 10^24 kg), and square the velocity (3,633,485,506,560,000,000,000 meter^2 / sec^2) then multiply together... you get 10,849,951,071,138,816 * 10^30 joules !

or 10 quattuordecillion, 849 tredecillion, 951 duodecillion, 71 undecillion, 138 decillion, 816 nonillion joules. (10,849,951,071,138,816,000,000,000,000,000,000,00 0,000,000,000 joules)

hope that helps tim (chris you didn't know that)

peter's answer is better however, since i used the formula for translational energy. my math was good but my physics not so much...

Yes, about 2.14×10^29 joules, or 48,000 billion megatons of TNT equivalent.

The energy of its motion around the sun is about 1000 times greater.