Question

beth just hopped on the edge of a merry - go - round. what are her linear and angular speeds if the diameter of the merry - go - round is 7 feet and it takes 5 seconds for it to make a complete revolution? round the solutions to two decimal places.

Explanation:

Step1: Calculate the angular speed

The formula for angular speed $\omega$ is $\omega=\frac{2\pi}{T}$, where $T$ is the period. The period $T = 5$ s.
$\omega=\frac{2\pi}{5}\text{ rad/s}\approx\frac{2\times3.14159}{5}= 1.26\text{ rad/s}$

Step2: Calculate the radius

The diameter $d = 7$ feet, so the radius $r=\frac{d}{2}=\frac{7}{2}=3.5$ feet.

Step3: Calculate the linear speed

The formula for linear speed $v$ is $v = r\omega$. We know $r = 3.5$ feet and $\omega=\frac{2\pi}{5}\text{ rad/s}$.
$v=3.5\times\frac{2\pi}{5}=\frac{7\pi}{5}\text{ ft/s}\approx\frac{7\times3.14159}{5}= 4.40\text{ ft/s}$

Answer:

Angular speed: $1.26$ rad/s, Linear speed: $4.40$ ft/s