Speeds of a Pulley and a Belt The pulley shown has a radius

Speeds of a Pulley and a Belt The pulley shown has a radius of 12.96 cm. Suppose it takes 18 sec for 56 cm of belt to go around the pulley. Find the linear speed of the belt in centimeters per second. Find the angular speed of the pulley in radians per second.

Solution

angular speed, omega= theta/t

theta=s/r=56/12.96=4.32 radians

angular speed, omega=theta/t=4.32/18=.24 radians per second

linear speed=omega * r= .24*12.96=3.11 cm per second