Earth's Rotation

* Period: 24 hours (one full rotation)

* Angular velocity (ω): 2π radians / 24 hours = π/12 radians/hour ≈ 0.262 radians/hour

Hour Hand of a Clock

* Period: 12 hours (one full rotation)

* Angular velocity (ω): 2π radians / 12 hours = π/6 radians/hour ≈ 0.524 radians/hour

Comparison

The hour hand of a clock has twice the angular velocity of the Earth rotating on its axis. This means the hour hand rotates twice as fast as the Earth.

Important Note: Angular velocity is a measure of how fast an object rotates, but it doesn't tell you how fast something moves *linearly*. The Earth's surface moves at a much higher speed than the tip of the hour hand due to its much larger radius.