Find the angular velocity, in rad/s, of the minute hand of a clock; the hour hand; the Earth about…

Step 1. (a) $T = 3600\ \text{s}$: $\omega = 1.745 \times 10^{-3}\ \text{rad/s}$.

Step 2. (b) $T = 12\ \text{h} = 43\,200\ \text{s}$: $\omega = 1.454 \times 10^{-4}\ \text{rad/s}$.

Step 3. (c) $T = 86\,400\ \text{s}$: $\omega = 7.27 \times 10^{-5}\ \text{rad/s}$.

Step 4. (d) $r = R\cos 60^\circ = 3.2 \times 10^{6}\ \text{m}$, so $v = \omega r = 233\ \text{m/s}$.