The Earth rotates once every 23 hours, 56 minutes and 4 seconds, which is called a sidereal day.

To calculate the angular velocity (ω) in radians per second, we can use the following formula:

ω = 2π / T

Where:

* ω is the angular velocity

* π is the mathematical constant pi (approximately 3.14159)

* T is the time period for one rotation (in seconds)

First, let's convert the sidereal day into seconds:

T = (23 hours * 3600 seconds/hour) + (56 minutes * 60 seconds/minute) + 4 seconds

T = 86164 seconds

Now, let's calculate the angular velocity:

ω = 2π / 86164 seconds

ω ≈ 7.2921 × 10⁻⁵ radians/second

Therefore, the angular velocity of the Earth around its own axis is approximately 7.2921 × 10⁻⁵ radians per second.