Question

A water wheel has a radius of 9 feet. The wheel is rotating at 5 revolutions per minute. Find the linear​ speed, in feet per​ minute, of the water.

Answer 1

`90\pi\text{ ft/s}\approx282.74\text{ ft/s}`

Explanation:

Refer to physics equation
`v=\omega r`, where
`\omega` is angular velocity.

Angular velocity's SI unit is rad/s. Convert rev/min to rad/s:

`\displaystyle 5\text{ rev/min}=5\cdot (1)/(60)\cdot 2\pi\approx 0.524\text{ rad/s}`

Now substitute
`\displaystyle\omega=(1\pi)/(6)` and
`r=9` into
`v=\omega r`:

`\displaystyle v=(1\pi)/(6)\cdot 9=(3)/(2)\pi\text{ ft/s}=\boxed{90\pi\text{ ft/s}}`