Question 2.SP.30: Two friction disks are shown in Fig. 2-22. Derive the expres......

The linear velocities of the mating points A and B on the two wheels are equal. If this were not true, the wheels would slip relative to each other. The linear velocities of points A and B are, respectively,

v_{A}=R_{1} \omega_{1} \qquad v_{B}=R_{2} \omega_{2}

But v_{A}=v_{B} if the drive is positive, i.e., without slip. Then

R_{1} \omega_{1}=R_{2} \omega_{2} \quad \text { or } \quad \frac{\omega_{1}}{\omega_{2}}=\frac{R_{2}}{R_{1}}