Chapter 6.1, Problem 125AYU

Pulleys Two pulleys, one with radius $r_1$ and other with radius $r_2$, are connected by a belt. The pulley with radius $r_1$ rotates at ${\omega }_1$ revolutions per minute, whereas the pulley with radius $r_2$ rotates at ${\omega }_2$ per minute. Show that

$\frac{r_1}{r_2}=\frac{{\omega }_2}{{\omega }_1}$