The average angular speed Wav is the average rate of change of the angular displacement.
The Earth's angular velocity is constant (or nearly constant). Therefore we can calculate the average angular velocity.
It takes 1 day to complete one rotation, total angular displacement is 2Π rad.
Time interval Δt = 1 day
Angular displacement of the Earth ΔΘ = 2Π rad
Average angular speed Wav of Earth is 2Π rad / day
Lets convert days to seconds
1 day = 24 hours = 24 x 3600 = 86400 seconds
Earth angular speed is 7.27x10-5 rad /s
Earth angular speed is 7.2921159 x 10-5 rad/s from:
World Book Encyclopedia Vol 6. Illinois: World Book Inc.: 1984: 12.
"It takes 23 hours 56 minutes 4.09 seconds for the Earth to spin around once 2Π radians/86164.09 seconds"
Note: The angular speed of a person near poles due to Earth's rotation is the same as that of someone near the equator, although the linear speeds are very different. Both move through the same angle in the same time interval, but the person near the equator moves through a much larger distance.