Answer to Question #286490 in Classical Mechanics for Meshe

Question

What is the angular displacement of a 0.7m diameter wheel that rolls 3m clockwise?

Answer 1

The arc traveled is given by

$S=\theta\;r$

Where.

$S=3\;m$ is the linear offset or arc traveled.

$r$ Is the radius.

$\theta$ Is the angular displacement.

The diameter is $d=0.7\;m$

The radius is half the diameter that is to say.

$r=\dfrac{d}{2}\\ r=\dfrac{0.7\;m}{2}\\ r=0.35\;m$

Obtaining the expression for the angular displacement.

$S=\theta\;r\\ \theta\;r=S\\ \theta=\dfrac{S}{r}\\$

Evaluating numerically.

$\theta=\dfrac{S}{r}\\ \theta=\dfrac{3.0\;m}{0.35\;m}\\ \theta=8.6\;rad$

The angular displacement is $\theta=8.6\;rad$