619 6.2 The Unit Circle and Circular Functions 121. 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. 12.96 cm (a) Find the linear speed of the belt in centimeters per second. (b) Find the angular speed of the pulley in radians per second. 122. Angular Speeds of Pulleys The two pulleys in the figure have radii of 15 cm and 8 cm, respectively. The larger pulley rotates 25 times in 36 sec. Find the angular speed of each pulley in radians per second. 15 cm 8 cm 123. Radius of a Spool of Thread A thread is being pulled off a spool at the rate of 59.4 cm per sec. Find the radius of the spool if it makes 152 revolutions per min. 124. Time to Move along a Railroad Track A railroad track is laid along the arc of a circle of radius 1800 ft. The circular part of the track subtends a central angle of 40°. How long (in seconds) will it take a point on the front of a train traveling 30.0 mph to go around this portion of the track? 125. Angular Speed of a Motor Propeller The propeller of a 90-horsepower outboard motor at full throttle rotates at exactly 5000 revolutions per min. Find the angular speed of the propeller in radians per second. 126. Linear Speed of a Golf Club The shoulder joint can rotate at 25.0 radians per sec. If a golfer’s arm is straight and the distance from the shoulder to the club head is 5.00 ft, find the linear speed of the club head from shoulder rotation. (Data from Cooper, J., and R. Glassow, Kinesiology, Second Edition, C.V. Mosby.) 127. Speed of an Ice Skate When performing the basic “Camel” move, a figure skater’s upper body and free leg are extended parallel to the ice. If the skater spins at the rate of 90 revolutions per minute and the distance from her or his hip to the tip of the extended ice skate is 40.0 in., how fast is the tip of the ice skate traveling? Give the answer in feet per second to the nearest tenth. 128. Speed of a Revolving Restaurant The revolving restaurant atop the Seattle Space Needle makes one revolution every 45 min. How fast is a diner seated 40 ft from the center of the restaurant moving? Give the answer in feet per minute to the nearest tenth. (Data from www.spaceneedle.com)
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