Question

A large globe spins with angular speed w. A smaller globe spins with double the angular speed. How does the period Tlarge of the globe compare with the period Tsmall of the of the small globe

Answer 1

The period Tlarge of the large globe is twice the period Tsmall of the small globe.

The period of a rotating object is the time it takes for the object to complete one full rotation. The period T of a rotating object is inversely proportional to its angular speed w, which is the rate at which it rotates. This means that when the angular speed of an object doubles, its period is halved.

In this case, the angular speed of the smaller globe is twice that of the larger globe. Therefore, the period of the smaller globe is half that of the larger globe. Mathematically, we can express this relationship as:

Tsmall = 2π / (2w) = π / w

Tlarge = 2π / w

Therefore, the period of the large globe is twice the period of the small globe.