SOL29 - Thevalingam Donald – Homework 29 – Due midnight – Inst Eslami 1 This print-out should have 16 questions Multiple-choice questions may

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Unformatted text preview: Thevalingam, Donald – Homework 29 – Due: Apr 27 2007, midnight – Inst: Eslami 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A wheel rotates about a fixed axis with an initial angular velocity of 77 rad / s. During a 6 s interval the angular velocity increases to 117 rad / s. Assume: The angular acceleration was con- stant during this time interval. How many revolutions does the wheel turn through during this time interval? Correct answer: 92 . 6282 . Explanation: First find α α = ω f- ω i Δ t = 6 . 66667 rad / s 2 . The total angle rotated in time t = 6 s is given by θ = ω t + 1 2 αt 2 = (77 rad / s)(6 s) + 1 2 (6 . 66667 rad / s 2 )(6 s) 2 = 582 rad . Finally, the number of revolutions rotated is simply N = θ 2 π = 92 . 6282 . keywords: 002 (part 1 of 1) 10 points A wheel starts from rest at t = 0 and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution in 8 . 7 s. How long after t = 0 will the wheel com- plete the second revolution? Correct answer: 12 . 3037 s. Explanation: In the conventional notation θ = s r ω = dθ dt = v r α = dω dt = a t r , we use “ θ- θ = ω t + 1 2 αt 2 ” at time t 1 to find the acceleration. The wheel starts from rest ( ω = 0) θ 1 = 0 + 1 2 αt 2 1 ⇒ α = 2 θ 1 t 2 1 = 0 . 166024 rad / s 2 . If we use the same equation again at time t 2 θ 2 = 0 + 1 2 αt 2 2 ⇒ t 2 = r 2 θ 2 α = s 2 θ 2 t 2 1 2 θ 1 = r θ 2 θ 1 t 1 = √ 2 t 1 , because we know θ 2 = 2 θ 1 (two revolutions). Notice that the result does not depend on how many revolutions the wheel went through, only the relative number of revolutions θ 2 θ 1 ....
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This note was uploaded on 03/04/2010 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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SOL29 - Thevalingam Donald – Homework 29 – Due midnight – Inst Eslami 1 This print-out should have 16 questions Multiple-choice questions may

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