Question 9.9: Rotational kinetic energy of the Earth Estimate the rotation...

From the Appendix, we find that I, the moment of inertia of a uniform sphere about an axis through its centre is given by I = 2M R²/5, where M is the mass of the sphere and R its radius. The kinetic energy of the Earth is therefore given by

T=\frac{1}{2} I \omega^{2}=\frac{1}{5} M R^{2} \omega^{2},

where M is the mass the Earth, R is its radius, and ω is its angular velocity.
On inserting the values M=6.0 \times 10^{24} kg , R=6400 km \text { and } \omega=7.3 \times 10^{-5} radians per second, T=2.6 \times 10^{29} J approximately.