99. = 26 inches; = 13 inches; = 35 mi/hr d r v 105. = 2.39 ×105 miles r rev/27.3 days = 35 mi ⋅ 5280 ft ⋅ 12 in. ⋅ 1 hr v hr mi ft 60 min = 2π radians/27.3 days = 36, 960 in./min π ω = 1 ω = = 36, 960 = v radians/hr 12 ⋅ in./min 27.3 13 in. r π 5 (2.39 ) ×10 ⋅ ≈ 2292 miles/hr ≈ 2843.08 radians/min 327.6 106. ≈ 2843.08 rad ⋅ 1 rev = 9.29 ×107 miles r min 2π rad ω = 1 rev/365 days ≈ = 452.5 rev/min v = 2π radians/365 days rω = 100. = 15 inches; r ω = 3 rev/sec = 6π rad/sec π 12 ⋅ 365 = = 15 ⋅ 6π in./sec = 90π ≈ 282.7 in/sec v rω (9.29 ) = = ×107 ⋅ π ≈ 66, 633 miles/hr v rω = 90π in. ⋅ 1ft ⋅ 1mi ⋅ 3600 sec ≈ 16.1 v 4380 mi/hr sec 12in. 5280ft 1hr = radians/hr = 3960 miles r 101. = 2 inches; = 8 inches; r r 107. θ = 35º 9 '− 29º 1 2 ω1 = 3 rev/min = 6π radians/min 57 ' ω2 = 5º12 ' Find : = v1 v2 = 5.2º = 5.2 ⋅ ω ω = r r π 180 1 1 2 2 ≈ 0.09076 radian 2(6π) = 8ω2 ⋅ 0.09076 ≈ 359 miles = 12π 8 2 = 3960 miles = 1.5π radians/min 102. r θ 1.5π = 38º 21'− 30º 20 ' = s ω = rθ 3960 = 8º1' = rev/min ≈ 8.017º 2π 3 = rev/min = 8.017 ⋅ π 4 180 ≈ 0.1399 radian
99. d = 26 inches; r = 13 inches; v = 35 mi/hr 105. r = 2.39 ×105 miles v = 35 mi ⋅ 5280 ft ⋅ 12 in. ⋅ 1 hr hr mi ft 60 min = 36, 960 in./min ω = 1 rev/27.3 days = 2π radians/27.3 days π ω = v = 36, 960 in./min = 12 ⋅ 27.3 radians/hr r 13 in. 5 π ≈ 2843.08 radians/min ≈ 2843.08 rad ⋅ 1 rev min 2π rad ≈ 452.5 rev/min 106. v = rω = (2.39 ×10 ) ⋅ ≈ 2292 miles/hr 327.6 r = 9.29 ×107 miles ω = 1 rev/365 days = 2π radians/365 days 100. r = 15 inches; ω = 3 rev/sec = 6π rad/sec π v = rω = 15 ⋅ 6π in./sec = 90π ≈ 282.7 in/sec v = 90π in. ⋅ 1ft ⋅ 1mi ⋅ 3600 sec ≈ 16.1 mi/hr sec 12in. 5280ft 1hr = radians/hr 12 ⋅ 365 v = rω = (9.29 ×107 ) ⋅ π ≈ 66, 633 miles/hr 4380 101. r = 3960 miles 107. r = 2 inches; r = 8 inches; θ = 35º 9 '− 29º 57 ' = 5º12 ' = 5.2º 1 2 ω1 = 3 rev/min = 6π radians/min Find ω2 : v1 = v2 = 5.2 ⋅ π r ω = r ω 180 ≈ 0.09076 radian 1 1 2 2 2(6π) = 8ω2 102. s = rθ = 3960 ⋅ 0.09076 ≈ 359 miles r = 3960 miles θ = 38º 21'− 30º 20 ' ω = 12π 2 8 = 1.5π radians/min 1.5π = 8º1' ≈ 8.017º = rev/min 2π 3 = 8.017 ⋅ π 180 = rev/min 4 ≈ 0.1399 radian
62514-0132318806_ISM_02-1.docx