Question

What is the angular displacement of a wheel that made 157.5revolutions? Round the answer to decimals.

Answer 1

To find the angular displacement, we have to transform 157.5 revolutions to radians. We know that 1 revolution equals 2pi radians

$1\text{rev}=2\pi$

Let's use the following proportion to find the angular displacement for 157.5 revolutions.

$\frac{1\text{rev}}{157.5\text{rev}}=\frac{2\pi}{x}$

Then, we solve for x

$\begin{gathered} x=\frac{2\pi\cdot157.5}{1} \\ x=315\pi \end{gathered}$

But, pi = 3.14, so

$\begin{gathered} x=315\cdot3.14\text{rad} \\ x=989.1rad \end{gathered}$

Therefore, the angular displacement is 989.1 radians.