Question

Determine the radius of a shift in decimeter of a pulley rotating at 300 revolution per minute when it drives another shaft rotation at 800 revolution per minutes having a diameter of 0.2m

Answer 1

The velocity $v$ of the point of contact on the pitch circles is the same on both gears, and is given by

$v=r_1\omega_1=r_2\omega_2$

So,

$\frac{r_1}{r_2}=\frac{\omega_2}{\omega_1}\to\frac{r_1}{r_2}=\frac{n_2}{n_1}\to r_1=r_2\frac{n_2}{n_1}=$

$=0.2\cdot\frac{800}{300}\approx0.53\ (m)$ . Answer