Length of the arc is , where is the radius of the circle and is the central angle.
Relation between linear speed of an object and angular speed of the object is , where is the radius of the circular motion and is measured in radians per unit time.
Angular speed , where is the angle generated by the object and is elapsed time.
Radius of the first pulley is .
Angular speed of first pulley is rpm.
Arc length of the first pully is .
Apply derivative on each side with respect to time.
= constant.
Radius of the second pulley is .
Angular speed of second pulley is rpm.
Arc length of the first pully is .
Apply derivative on each side with respect to time.
= constant.
Since the two pulleys have constant linear speed, equate the velocities.
.
.
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