603 6.1 Radian Measure 82. Gear Movement Repeat Exercise 81 for gear radii of 4.8 in. and 7.1 in. and for an angle of 315° for the smaller gear. 83. Rotating Wheels The rotation of the smaller wheel in the figure causes the larger wheel to rotate. Through how many degrees does the larger wheel rotate if the smaller one rotates through 60.0°? 84. Rotating Wheels Repeat Exercise 83 for wheel radii of 6.84 in. and 12.46 in. and an angle of 150.0° for the smaller wheel. 85. Rotating Wheels Find the radius of the larger wheel in the figure if the smaller wheel rotates 80.0° when the larger wheel rotates 50.0°. 86. Rotating Wheels Repeat Exercise 85 if the smaller wheel of radius 14.6 in. rotates 120.0° when the larger wheel rotates 60.0°. 87. Pulley Raising a Weight Refer to the figure. (a) How many inches will the weight in the figure rise if the pulley is rotated through an angle of 71° 50′? (b) Through what angle, to the nearest minute, must the pulley be rotated to raise the weight 6 in.? 8.16 cm 5.23 cm 11.7 cm r 9.27 in. 88. Pulley Raising a Weight Find the radius of the pulley in the figure if a rotation of 51.6° raises the weight 11.4 cm. r 89. Bicycle Movement The figure shows the chain drive of a bicycle. How far will the bicycle move if the pedals are rotated through 180.0°? Assume the radius of the bicycle wheel is 13.6 in. 1.38 in. 4.72 in. 90. Car Travel The speedometer of Terry’s Honda CR-V is designed to be accurate with tires of radius 14 in. (a) Find the number of rotations of a tire in 1 hr if the car is driven at 55 mph. (b) Suppose that oversize tires of radius 16 in. are placed on the car. If the car is now driven for 1 hr with the speedometer reading 55 mph, how far has the car gone? If the speed limit is 55 mph, does Terry deserve a speeding ticket?
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