Question

Pulleys Two pulleys, one with radius $r_1$and the other with radius $r_2$, are connected by a belt. The pulley with radius $r_1$rotates at $v_1$revolutions per minute, whereas the pulley with

radius $r_2$rotates at $v_2$revolutions per minute. Show thatrole="math" localid="1646296862603" $\frac{r_1}{r_2}=\frac{{\omega }_1}{{\omega }_2}$

Short answer

The relationship between the radius and angular speed of two pulleys is$\frac{r_1}{r_2}=\frac{{\omega }_1}{{\omega }_2}$

Step-by-step solution

Step 1. Given Information 

Two pulleys with radius $r_1$and $r_2$are connected by a belt.

We have to prove the relation$\frac{r_1}{r_2}=\frac{{\omega }_1}{{\omega }_2}$