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Unformatted text preview: agnew (ja26385) – oldmidterm 03 – Turner – (58220) 1 This printout should have 24 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A rotating bicycle wheel has an angular speed of 70 ◦ / s at 3 . 2 s and a constant angular acceleration of 32 ◦ / s 2 . With the center of the wheel at the origin, the valve stem is on the positive xaxis (horizontal) at t = 1 . 5 s. Through what angle has the valve stem turned between 1 . 5 s and 8 . 2 s? Correct answer: 822 . 76 ◦ . Explanation: Let : ω 1 = 70 ◦ / s , t 1 = 3 . 2 s , α = 32 ◦ / s 2 , θ = 0 ◦ , t = 1 . 5 s , and t = 8 . 2 s . The initial angular velocity can be deter mined from ω 1 = ω + α ( t 1 − t ) ω = ω 1 − α ( t 1 − t ) = 70 ◦ / s − (32 ◦ / s 2 ) (3 . 2 s − 1 . 5 s) = 15 . 6 ◦ / s . This θ 2 = ω ( t 2 − t ) + 1 2 α ( t 2 − t ) 2 = (15 . 6 ◦ / s) (8 . 2 s − 1 . 5 s) + 1 2 (32 ◦ / s 2 ) (8 . 2 s − 1 . 5 s) 2 = 822 . 76 ◦ . 002 (part 1 of 3) 10.0 points A beetle takes a joy ride on a pendulum. The string supporting the mass of the pendulum is 178 cm long. If the beetle rides through a swing of 45 ◦ , how far has he traveled along the path of the pendulum? Correct answer: 139 . 801 cm. Explanation: Let : r = 178 cm , and θ = 45 ◦ . Arc length is defined as s = r θ = (178 cm)(45 ◦ ) · parenleftBig π 180 ◦ parenrightBig = 139 . 801 cm . 003 (part 2 of 3) 10.0 points What is the displacement experienced by the beetle while moving theough the same angle 45 ◦ ? Correct answer: 136 . 235 cm. Explanation: Using the law of cosines, we have bardbl vector R bardbl = radicalbig r 2 + r 2 − 2 r r cos θ = r radicalbig 2 (1 − cos θ ) = (178 cm) radicalbig 2(1 − cos 45 ◦ ) = 136 . 235 cm . Alternative Solution: Divide the isosce les triangle in half. Then bardbl vector R bardbl = 2 . r sin parenleftbigg θ 2 parenrightbigg = 2 . 0 (178 cm) sin22 . 5 ◦ = 136 . 235 cm . 004 (part 3 of 3) 10.0 points If the pendulum at some instant is swinging at 2 . 3 rad / s, how fast is the beetle traveling? Correct answer: 409 . 4 cm / s. Explanation: agnew (ja26385) – oldmidterm 03 – Turner – (58220) 2 Let : ω = 2 . 3 rad / s . Linear and angular velocity are related by v = r ω = (178 cm)(2 . 3 rad / s) = 409 . 4 cm / s . keywords: 005 10.0 points At t = 0, a wheel rotating about a fixed axis at a constant angular deceleration of 0 . 82 rad / s 2 has an angular velocity of 2 . 9 rad / s and an angular position of 7 . 7 rad. What is the angular position of the wheel after 3 s? Correct answer: 12 . 71 rad. Explanation: Let : α = − . 82 rad / s 2 , ω = 2 . 9 rad / s , θ = 7 . 7 rad , and t = 3 s ....
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This note was uploaded on 05/11/2010 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.
 Spring '08
 Turner
 Physics

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