Two pulleys have radii 20cm and 6cm,respectively. The smaller pulley rotates 15 times in 12 seconds. Find the angular speed of each pulley in rad/sec

2 answers

15rev/12sec = 5/4 rev/sec = 5π/2 rad/s
That's the speed of the smaller pulley

Assuming they are both attached to the same belt, the larger pulley's rotational speed is 6/20 the speed of the smaller one.
Smaller Pulley:
V=15rev/12s * 6.28rad/rev = 7.85 rad/s

Larger Pulley:
V = (6cm/20cm) * 7.85 = 2.36 rad/s.