The 2 pulleys in the figure have radii of 15 cm and 8 cm, respectively. The larger pulley rotates 25 times in 36 seconds find the angular velocity of each pulley in radians per second. Find angular velocity of each pulley in radians per second.

Answer 1

2π(15)/(2π(8)) = 1.875 or 15/8

so for each rotation of the large pulley, the smaller rotates 1.875 times or 15/8 times.

angular velocity of large one = 25(2π)/36 radians per second
= 25π/18 rad/s

angular velocity of smaller = (15/8)(25π/18) rad/s
= 125π/48 rad/s

Answer 2

4.36 rad/sec