Answer: To find the Earth's angular velocity in rad/s, we need to know the time taken for one complete rotation (period) of the Earth around its own axis.
The formula for angular velocity (ω) is given by:
ω = 2π / T
where:
ω = angular velocity in rad/s
T = period of rotation in seconds
The period of rotation is the time taken for the Earth to complete one full rotation, which is approximately 24 hours (86,400 seconds) for a sidereal day. A sidereal day is the time taken for the Earth to rotate 360 degrees with respect to the stars.
Now, let's calculate the Earth's angular velocity:
ω = 2π / T
ω = 2π / 86,400 s
ω ≈ 7.27 × 10^(-5) rad/s
The Earth's angular velocity around its own axis is approximately 7.27 × 10^(-5) rad/s.