Question

A wheel rotates at 16 rad/s. How many revolutions does it complete in 7 seconds?

Answer 1

Given

Rotational speed

ω = 16 rad/s

Time

t = 7s

Procedure

First, let's calculate the radial travel of the wheel in 7 seconds.

`\begin{gathered} 16\text{ rad/s}\cdot7\text{ s} \\ 112\text{ rad} \end{gathered}`

Now let's convert those radians into revolutions

`\begin{gathered} 112\text{ rad}\cdot\frac{2\pi}{1\text{ rad}} \\ 17.8\text{ rev} \end{gathered}`

Answer

The wheel would rotate a total of 17.8 revs in the 7 sec.