617 6.2 The Unit Circle and Circular Functions Suppose that point P is on a circle with radius r, and ray OP is rotating with angular speed v. Use the given values of r, v, and t to do the following. See Example 5. (a) Find the angle generated by P in time t. (b) Find the distance traveled by P along the circle in time t. (c) Find the linear speed of P. 81. r = 20 cm, v = p 12 radian per sec, t = 6 sec 82. r = 30 cm, v = p 10 radian per sec, t = 4 sec 83. r = 8 in., v = p 3 radians per min, t = 9min 84. r = 12 ft, v = 8p radians per min, t = 5 min Use the formula v = u t to find the value of the missing variable. 85. v = 2p 3 radians per sec, t = 3 sec 86. v = p 4 radian per min, t = 5min 87. u = 3p 4 radians, t = 8 sec 88. u = 2p 5 radians, t = 10 sec 89. u = 2p 9 radian, v = 5p 27 radian per min 90. u = 3p 8 radians, v = p 24 radian per min Use the formula v = rv to find the value of the missing variable. 91. r = 12m, v = 2p 3 radians per sec 92. r = 8 cm, v = 9p 5 radians per sec 93. v = 9 m per sec, r = 5 m 94. v = 18 ft per sec, r = 3 ft 95. v = 12 m per sec, v = 3p 2 radians per sec 96. v = 24 cm per sec, v = 2p 3 radian per sec The formula v = u t can be rewritten as u = vt. Substituting vt for u converts s = ru to s = rvt. Use the formula s = rvt to find the value of the missing variable. 97. r = 6 cm, v = p 3 radians per sec, t = 9 sec 98. r = 9 yd, v = 2p 5 radians per sec, t = 12 sec 99. s = 6p cm, r = 2 cm, v = p 4 radian per sec 100. s = 12p 5 m, r = 3 2 m, v = 2p 5 radians per sec 101. s = 3p 4 km, r = 2 km, t = 4 sec 102. s = 8p 9 m, r = 4 3 m, t = 12 sec Find the angular speed v for each of the following. 103. the hour hand of a clock 104. the second hand of a clock 105. the minute hand of a clock 106. a gear revolving 300 times per min 107. a wind turbine with blades turning at a rate of 15 revolutions per minute 108. a point on Earth’s equator moving due to Earth’s rotation
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