Explanation

(a) $\omega_{1} = 2\pi\ rad/day$, $\omega_{2} = 0$ and $t = 1\ day$
$\therefore\alpha = \frac{\omega_{2} - \omega_{1}}{t} = \frac{0 - 2\pi}{1} = 2\pi\frac{rad}{day^{2}} = \frac{2\pi}{(86400)^{2}}\frac{rad}{s^{2}}$
Torque required to stop the earth $\tau = I\alpha = FR$
$\Rightarrow F = \frac{I\alpha}{R} = \frac{\frac{2}{5}MR^{2} \times \alpha}{R} = \frac{2}{5}MR \times \alpha$
$= \frac{2}{5} \times 6 \times 10^{24} \times 6400 \times 10^{3} \times \frac{2\pi}{(86400)^{2}} = 1.3 \times 10^{22}N$