# Angular Speed

## The rate change of the radial angle for an object moving in a circle.

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Practice Angular Speed

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Fast and Slow on one Merry-go-round?

### Why do you feel a different speed in a different part of a Merry-go-Round?

A typical Merry-go-Round in an amusement park [Figure1]

Angular speed is the the rate at which the angle changes, just like how linear speed is the rate at which the position changes. A rotating object is said to have a high angular speed when the rate at which the angle changes is fast. In relation to the angular position, angular speed is its first derivative.

For a rolling object, angular speed depends on its linear velocity and its radius. To solve for angular speed, it is simply the linear velocity divided by its radius. Thus, we have the following formula established:

\begin{align*}\omega\end{align*}= V/ R

In amusement parks, engineers use the concept of angular speed to design many rides, one of which is the Merry-go-Round.

### Creative Applications

1. How is the physics of the Merry-go-Round different from any rolling object?

2. Using your knowledge of angular speed, explain why Merry-go-Round have large radiuses.

3. What is the importance of limiting the angular speed of the Merry-go-Round? In other words, why is it bad for us if the angular speed is too high?

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