Final answer:
The average angular velocity of the Earth as it rotates on its axis is 2π radians/day, which is option (b) 2π rad/day.
Step-by-step explanation:
The question is asking about the average angular velocity of the Earth as it rotates on its axis. The Earth completes one full rotation (360 degrees or 2π radians) every 24 hours. Angular velocity (w) is the rate of change of the angle with respect to time; it is given by the formula w = Θ/t, where Θ is the angle in radians and t is the time in seconds for a complete rotation.
To calculate the angular velocity of Earth, we take the angle of a full rotation, which is 2π radians, and divide it by the period of rotation in seconds. Since there are 24 hours in a day and 3600 seconds in an hour, the period of rotation is 24 * 3600 seconds. The calculation would be w = 2π radians / (24 * 3600 seconds), but since we are looking for the angular velocity in radians per day, we can simplify this to w = 2π radians / 1 day.
Therefore, the average angular velocity of Earth as it rotates on its axis is 2π radians/day, which corresponds to choice (b) 2π rad/day.