Pre-Calculus, 9th edition
117

 PAGE: 363 SET: Exercises PROBLEM: 117

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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