HW09-solutions - Le(tl8426 – HW09 – gentle –(56245 1...

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Unformatted text preview: Le (tl8426) – HW09 – gentle – (56245) 1 This print-out should have 33 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A ladybug sits at the outer edge of a merry- go-round, and a gentleman bug sits halfway between her and the axis of rotation. The merry-go-round makes a complete revolution once each second. What is the gentleman bug’s angular speed? 1. twice the ladybug’s 2. impossible to determine 3. the same as the ladybug’s correct 4. half the ladybug’s Explanation: Angular speed is the same for every point on the merry-go-round. 002 (part 1 of 5) 10.0 points A wheel starts from rest with constant angu- lar acceleration of 3 . 7 rad / s 2 . After 1 . 9 s, what is its angular velocity? Correct answer: 7 . 03 rad / s. Explanation: Let : ω = 0 , α = 3 . 7 rad / s 2 , and t = 1 . 9 s . The angular velocity is ω = ω + αt = αt = (3 . 7 rad / s 2 ) (1 . 9 s) = 7 . 03 rad / s . 003 (part 2 of 5) 10.0 points Through what angle did the wheel turn? Correct answer: 6 . 6785 rad. Explanation: Δ θ = ω Δ t + 1 2 α (Δ t ) 2 = 1 2 α (Δ t ) 2 = 1 2 (3 . 7 rad / s 2 ) (1 . 9 s) 2 = 6 . 6785 rad . 004 (part 3 of 5) 10.0 points Through how many revolutions did the wheel turn? Correct answer: 1 . 06292 rev. Explanation: Δ θ = (6 . 6785 rad) parenleftbigg 1 rev 2 π rad parenrightbigg = 1 . 06292 rev . 005 (part 4 of 5) 10.0 points What is the speed of a point 0 . 1 m from the axis of rotation? Correct answer: 0 . 703 m / s. Explanation: Let : r = 0 . 1 m . The tangential speed is v = r ω = (0 . 1 m) (7 . 03 rad / s) = 1 . 06292 rev . 006 (part 5 of 5) 10.0 points What is the acceleration of a point 0 . 1 m from the axis of rotation? Correct answer: 4 . 95592 m / s 2 . Explanation: Let : r = 0 . 1 m . Le (tl8426) – HW09 – gentle – (56245) 2 The acceleration has two components, the tangential and the centripetal acceleration, which act perpendicular to each other: a = radicalBig a 2 t + a 2 c = radicalBig ( r α ) 2 + ( r ω 2 ) 2 = r radicalbig α 2 + ω 4 = (0 . 1 m) × radicalBig (3 . 7 rad / s 2 ) 2 + (7 . 03 rad / s) 4 = . 703 m / s . keywords: 007 (part 1 of 3) 10.0 points A car accelerates uniformly from rest and covers a distance of 78 m in 8 . 4 s. If the diameter of a tire is 31 cm, find the angular acceleration of the wheel. Correct answer: 14 . 2638 rad / s 2 . Explanation: Let : Δ x = 78 m , Δ t = 8 . 4 s , and R = 15 . 5 cm = 0 . 155 m . From kinematics, Δ x = 1 2 a Δ t 2 a = 2 Δ x Δ t 2 , so a = Rα α = a R = 2 Δ x R (Δ t ) 2 = 2 (78 m) (0 . 155 m) (8 . 4 s) 2 = 14 . 2638 rad / s 2 . 008 (part 2 of 3) 10.0 points Find the final angular velocity of one of the car’s wheels....
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HW09-solutions - Le(tl8426 – HW09 – gentle –(56245 1...

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