Calculating Kinetic Energy for Rotating Planets

[Bjarne]

How can the kinetic energy of a rotaing planet be calculate?
I know the KE equation, - but how can I calculated the mass momentum (average speed) of the mass of a rotating body.

 

[mgb_phys]

http://en.wikipedia.org/wiki/Rotational_kinetic_energy
You probably have to make some assumptions that the planet is a uniform solid sphere (a bit of an overestimate for a real planet)

 

[D H]

You probably have to make some assumptions that the planet is a uniform solid sphere (a bit of an overestimate for a real planet)

Alternatively, do a google search for the Earth's moment of inertia. The simplistic assumption of a uniform sphere yields a value that is off by more than 20%. In other words, while it is in the right ball park, it is not very good.

 

[Pinu7]

According to The Earth's Variable Rotation- Kurt Lambeck, the moment of inertia of the Earth around its polar axis is about

I=8.034(10^36) kg m^2

Remember
Kinetic Energy=Rotational Kinetic Energy+Translational Kinetic Energy

The TKE will vary because the translational speed of the Earth varies along its orbit. However, the average velocity is about 29,800 m/s (lenghth of orbit/365 days) so that $$KE=RKE+TKE=\frac{1}{2}(I\omega ^{2}+mv^{2})$$
plug the numbers in yourself.

 

[mgb_phys]

Alternatively, do a google search for the Earth's moment of inertia..

Nobody said anything about Earth !

 

[D H]

Nobody said anything about Earth !

Fine. Look up the moment of inertia for any planet. The uniform density assumption overstates the moment of inertia for the Sun by almost an order of magnitude, the gas giants by 60% to 100%, and the terrestrial planets by 10% (Mars) to 20% (Earth).