Radians

[sherriekay]

A circular irrigation has a diameter of 25.0 m and completes one cirlce 5 times each hour. through how many radians does the irrigation move in 30.0 min?

 

[soroban]

Hello, sherriekay!

A circular irrigation has a diameter of 25.0 m and completes one circle 5 times each hour.
Through how many radians does the irrigation move in 30.0 min?

It's sort of a trick question. .The diameter is completely irrelevant.

\(\displaystyle \text{The object turns 5 complete circles every hour.}\)
. . \(\displaystyle \text{That is: }\:5(2\pi) =10\pi \text{ radians each hour.}\)

\(\displaystyle \text{In 30 minutes}\left(\tfrac{1}{2}\text{ hour})\text{, it turns }5\pi\text{ radians.}\)