## Precalculus (6th Edition) Blitzer

First, calculate the angular speed of the carousel in radians per minute. To calculate the angular speed of the carousel in radians per minute, multiply the angular speed in revolutions per minute with $2\pi$ radians. So, the angular speed of the carousel in radians per minute is: $\left( 2.5\ \text{rev/min} \right)2\pi \ \text{rad}=5\pi \ \text{rad/min}$ And the linear speed $v$ is the product of the angular speed and the radius of the circle formed by the rotation of the child seated on the animal. It is given as: $v=r\omega$ Here, $r$ is the distance by which the child seated on the animal is away from the center of the carousel and $\omega$ is the angular speed of the carousel. Put $5\pi$ radians per minute for $\omega$: \begin{align} & v=r\left( 5\pi \ \text{rad/min} \right) \\ & =5\pi r\ \text{rad/min} \end{align} Hence, the linear speed of the child seated on the carousel can be calculated by the above relation.