The average angular velocity of the spinning of the earth is

${\omega }_{avg}=\frac{2{\pi }^c}{24\text{hours}}$

we know average angular velocity $=\frac{2{\pi }^c}{\text{Time\hspace{0.17em}period}}$

$=\frac{2\pi }{24\times 60\times 60}=\frac{\pi }{12\times 3600}=\frac{\pi }{43,200}\text{rad/s}$