## Physics: Principles with Applications (7th Edition)

$$\frac{\omega_1}{\omega_2} = \frac{R_2}{R_1}$$
The tangential speed of the turntable equals the tangential speed of the roller because there is no slipping between the surfaces. $$v_1=v_2$$ $$\omega_1 R_1=\omega_2 R_2$$ $$\frac{\omega_1}{\omega_2} = \frac{R_2}{R_1}$$