Question

If earth suddenly stop rotating and all its rotational KE is used up in raising it temperature and it s is taken to be the specific heat capacity of earth, the rise in temperature of earth, the rise in temperature of earth will be(R- radius of the earth and w angular velocity of rotation)?

Answer 1

Rotational kinetic energy of earth =$\frac{1}{2}I{w}^2$
Moment of inertia of earth I=$\frac{2}{5}M{R}^2$
M=mass of earth, s= specific heat capacity of earth , w= angular velocity
Kinetic energy of earth is equal to change in its heat energy
According to law of thermodynamic $$\begin{gathered} ∆\theta =Ms∆T \\ \frac{1}{2}\left(\frac{2}{5}M{R}^2\right)w^2=Ms∆T \\ ∆T=\frac{R^2{w}^2}{5s} \\ changeinearth\text{'}stemperatureis\frac{R^2{w}^2}{5s} \end{gathered}$$