# The earth of mass m , radius r  is revolving around sun in an orbit of radius D with an angular velocity ω and rotating around itself with an angular velocity ω' . What is the total kinetic energy of the earth ?

24 Points
12 years ago

Hi,

It sometimes is convenient to split the total kinetic energy of a body into the sum of the body's center-of-mass translational kinetic energy and the energy of rotation around the center of mass (rotational energy):

$E_k = E_t + E_r \,$

where:

Ek is the total kinetic energy
Et is the translational kinetic energy
Er is the rotational energy or angular kinetic energy in the rest frame

=.5mω2D+ .5I(ω')2

where, I = moment of inertia