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Homework 11 - Practice Problems; Rotation. Fluids-solutions

# Homework 11 - Practice Problems; Rotation. Fluids-solutions...

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sanchez (es25396) – Homework 11 - Practice Problems; Rotation. Fluids – guevara – (130101) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. 001 (part 1 o± 2) 10.0 points A uni±orm solid disk and a uni±orm hoop are placed side by side at the top o± an incline o± height h . I± they are released ±rom rest and roll with- out slipping, determine their speeds when they reach the bottom. ( d = disk, h = hoop) 1. v d = r 4 3 hg , v h = R hg correct 2. v d = R hg , v h = R 2 hg 3. v d = r 1 2 hg , v h = r 1 3 hg 4. v d = r 2 3 hg , v h = R 3 hg 5. v d = R 2 hg , v h = R hg Explanation: Because they roll without slipping, v = r ω and the total kinetic energy is K = 1 2 mv 2 + 1 2 I ω 2 , so ±or the disk, since I = 1 2 mr 2 , K = 1 2 mv 2 d + 1 4 mv 2 d = 3 4 mv 2 d . 3 4 mv 2 d = mhg , v d = r 4 3 hg . Similarly, ±or the hoop, since I = mr 2 con- servation o± energy gives us v h = R hg . 002 (part 2 o± 2) 10.0 points Which object reaches the bottom frst? 1. the disk correct 2. the hoop 3. both at the same time Explanation: From the previous result one can see that ±or any ±allen height h , the disk has a velocity greater than the velocity o± the hoop, so the disk will reach the bottom frst (its velocity has been greater than hoop’s all the time). keywords: 003 10.0 points A fgure skater on ice spins on one ±oot. She pulls in her arms and her angular speed in- creases. Choose the best statement below. 1. Her angular speed increases because her potential energy increases as her arms come in. 2. Her angular speed increases because air ±riction is reduced as her arms come in. 3. Her angular speed is unrelated to her arms. She pulls them in at the same time as she speeds up her spin because it looks better this way. 4. Her angular speed increases because by pulling in her arms she creates a net torque in the direction o± rotation. 5. Her angular speed increases because her angular momentum increases. 6. Her angular speed increases because her angular momentum remains the same but her moment o± inertia decreases. correct 7. Her angular speed increases because she is undergoing uni±ormly accelerated angular motion. Explanation: When a skater spins on one ±oot — or rather on just the toe o± one skate — the external

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sanchez (es25396) – Homework 11 - Practice Problems; Rotation. Fluids – guevara – (130101) 2 forces acting on her produce no net torque because of zero lever arms. Consequently, the skater’s angular momentum is conserved, L = I ω = const . When the skater pulls in her arms, her mo-
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Homework 11 - Practice Problems; Rotation. Fluids-solutions...

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