Classical Mechanics
# Angular Kinematics

A ceiling fan is switched off and, after 36 rotations, its angular velocity falls by half.

How many more rotations will it make before coming to rest?

**Details and Assumptions**

- The angular deceleration of the fan is uniform.

Geostationary satellites orbit at a height of $35,786~\mbox{km}$ above the Earth's surface and orbit with the same period as the Earth (so they always stay above the same spot, i.e. geostationary). If you stand on the Earth's surface what is the ratio of a geostationary satellite's speed to your speed?

**Details and assumptions**

- Assume the earth is a perfect sphere of radius 6370 km.
- We're asking about tangential speeds in this question (in m/s), not angular velocities.

At the playground, there is a merry-go-round initially at rest, whose moment of inertia is $1320 \text{ kg} \cdot \text{m}^2.$ A boy weighing $33 \text{ kg}$ stands on it, and his distance from the center of the merry-go-round is $8$ meters. If the boy begins to run in a circular path (about the center of the merry-go-round) with a speed of $6.0 \text{ m/s}$ relative to the ground, what is the angular speed of the merry-go-round?

Ignore any friction other than that between the surface of the merry-go-round and the boy.