Question

Tenemos una polea conductora de 80 mm de diámetro que gira a 600 rpm, unida mediante correa a una polea conducida de 20 mm. ¿Qué velocidad adquiere la polea conducida?

Answer 1

w2 = 2400 rpm

v2 = 48 m/min

Step-by-step explanation:

You take into account that both pulleys have the same tangential velocities, that is:

`v_1=v_2` (1)

Furthermore, v is related to the angular frequency of the pulleys by the following equation:

`v_1=\omega_1r_1\\\\v_2=\omega_2r_2\\`

Next, you replace v1 and v2 in (1) and you do w2 the subject of the formula:

`\omega_1r_1=\omega_2r_2\\\\\omega_2=(r_1)/(r_2)\omega_1\\\\\omega_2=(80mm)/(20mm)(600rpm)=2400\ rpm`

The angular velocity is 2400 rpm

And the tangetial velocity is:

v2 = w2r2 = (2400)(20mm) = 48000 mm/min = 48 m/min