A Ferris wheel starts spinning at $t = 0$ s and stops at $t = 12$ s. The Ferris wheel makes 4 loops during that time. We are asked to find the angular speed, which is represented by $k$.

1. Problem Description

A Ferris wheel starts spinning at $t = 0$ s and stops at $t = 12$ s. The Ferris wheel makes 4 loops during that time. We are asked to find the angular speed, which is represented by $k$.

2. Solution Steps

A loop is a full rotation, which is equal to $2\pi$ radians.

Since the Ferris wheel made 4 loops, the total angle rotated is $4 \times 2\pi = 8\pi$ radians.

The time taken to complete these 4 loops is $12$ seconds.

The angular speed $k$ is the total angle rotated divided by the time taken.

So, $k = \frac{8\pi}{12} = \frac{2\pi}{3}$ radians per second.

3. Final Answer

$k = \frac{2\pi}{3}$