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If you shrunk to the size of an ant, and were forced to live on the second hand of a wristwatch, it would behoove you to understand movement in a circle. Prepare for the worst with Angular Kinematics.

When a ceiling fan is switched off, its angular velocity reduces to half after it making 36 rotations. How many more rotations will it make before coming to rest?

**Details and Assumptions**

- Angular deceleration of the fan is uniform.

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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.

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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.

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