Q: What is the linear velocity of a person at equator of the earth to its spinning motion ? (Radius of the earth = 6400 km).

Sol. The earth completes one rotation in 24 hour. Its angular velocity.

$\large \omega = \frac{2\pi N}{t}$

$\large \omega = \frac{2\pi \times 1}{24 \times 60 \times 60} =\frac{\pi}{43,200} rad/s $

The linear velocity,

$\large v = r \omega = 6.4 \times 10^6 \times \frac{\pi}{43,200} $

= 465.5 m/s