Calculate approximately the average angular velocity of the earth about its axis of rotation.

Sure, to calculate the average angular velocity of the Earth about its axis of rotation, we need to know that the Earth completes one full rotation (360 degrees) in approximately 24 hours.

Step 1: Convert 24 hours to seconds because the standard unit of angular velocity is radians per second. There are 60 seconds in a minute and 60 minutes in an hour, so 24 hours is 24 * 60 * 60 = 86,400 seconds.

Step 2: Convert the full rotation of the Earth (360 degrees) to radians. There are 2π radians in a full circle (360 degrees), so one full rotation is 2π radians.

Step 3: The average angular velocity (ω) is the total angle θ (in radians) divided by the total time t (in seconds). So, ω = θ / t.

Step 4: Substituting the values we have, ω = 2π / 86,400 ≈ 0.0000727 radians per second.

So, the average angular velocity of the Earth about its axis of rotation is approximately 0.0000727 radians per second.