Answer:
w2 = 2400 rpm
v2 = 48 m/min
Explanation:
You take into account that both pulleys have the same tangential velocities, that is:
[tex]v_1=v_2[/tex] (1)
Furthermore, v is related to the angular frequency of the pulleys by the following equation:
[tex]v_1=\omega_1r_1\\\\v_2=\omega_2r_2\\[/tex]
Next, you replace v1 and v2 in (1) and you do w2 the subject of the formula:
[tex]\omega_1r_1=\omega_2r_2\\\\\omega_2=\frac{r_1}{r_2}\omega_1\\\\\omega_2=\frac{80mm}{20mm}(600rpm)=2400\ rpm[/tex]
The angular velocity is 2400 rpm
And the tangetial velocity is:
v2 = w2r2 = (2400)(20mm) = 48000 mm/min = 48 m/min
