9. h = R. 10. h = 3 R
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1 Version PREVIEW Torque Chap. 8 sizeore (13756) 1 This print-out should have 3 questions. ultiple-choice questions ay continue on the next colun or page find all choices before answering. Note in the dropped rod proble the rod falls sideways. Roller Coaster points Consider a frictionless roller coaster such as depicted below. h C B D Passenger cars start at point C with zero initial speed, accelerate as they go down, swing around a circular vertical loop, then go on towards further adventures (not shown). When a car goes through the top of the loop (point B), the passengers feel weightless (for just a oent). What is the height h of the starting point C? 1. h 3 R 2. h 2 R 3. h 7 2 R. h 5 2 R correct 5. h 1 R 6. h 2 3 R 7. h 7 3 R 8. h 1 3 R R A 9. h R 10. h 3 R Auseent Park Rocket Ride 002 (part 1 of ) 10.0 points An auseent park builds a ride in which the victi is ade to spin about a pole with a rocket strapped on his seat. The rider, box and rocket have an initial total ass of 160 kg. Neglect the ass of the rod of length. 160 kg 89 N 320 /s What is the oent of inertia of rider, box and rocket about the pole? The acceleration of gravity is 9.8 /s 2. Treat the rider, box and rocket as a point ass. Correct answer: 2560 kg (part 2 of ) 10.0 points The rocket develops a thrust of 89 N perpendicular to the path of the rider. What is the initial angular acceleration of the rider? Correct answer: rad/s (part 3 of ) 10.0 points After what tie t is the rider s velocity equal to 7 /s? Neglect the change in ass of the rocket. Correct answer: s. 005 (part of ) 10.0 points Gas exits the rocket at v t 320 /s. What ass per second ust leave to develop the thrust given above? Correct answer: kg/s. Baseball Energies
2 Version PREVIEW Torque Chap. 8 sizeore (13756) points The center of ass of a pitched baseball or radius 5.63 c oves at 59.8 /s. The ball spins about an axis through its center of ass with an angular speed of 62.5 rad/s. Calculate the ratio of the rotational energy to the translational kinetic energy. Treat the ball as a unifor sphere. Correct answer: Car Engine Horsepower points An autoobile engine develops a torque of 10 N and is rotating at a speed of 000 rev/in. What horsepower does the engine generate? 1 hp 76 W. Correct answer: hp. Rod Plus Weight 008 (part 1 of 3) 10.0 points A unifor rod has length 0 and ass 9 kg. A ass of 9 kg is attached at one end. The other end of the rod is pivoted about the horizontal axis at O. pivot O 9 kg 0 9 kg 9 kg 9 kg 56 Deterine the torque about O iediately after the rod-plus-ass syste is released fro the horizontal position. The acceleration of gravity is 9.8 /s 2. Correct answer: 5292 kg 2 /s (part 2 of 3) 10.0 points After the rod-plus-ass syste is released, it rotates freely about the point O. Deterine its angular velocity ω as the rod passes through the vertical direction. Correct answer: s (part 3 of 3) 10.0 points The angle between the instantaneous position of the rod and the initial horizontal direction is 56. How uch potential energy is released in going fro 0 to 56? Correct answer: J. Rope Around Cylinder points A assless rope is wrapped around a unifor cylinder of radius R and ass. What is the linear acceleration of the cylinder? Assue the unwrapped portion of the rope is vertical and the axis of the cylinder reains horizontal. 1. a 3 g 5 2. a 2 g 5 3. a g. a 2 g 3 correct 5. a 2 g 6. a g 3 7. a 3 g 8. a g 2 9. a g ω R
3 Version PREVIEW Torque Chap. 8 sizeore (13756) a g 5 Wind Vane points A bright physics student purchases a weather vane for her father s garage. The vane consists of a rooster sitting on top of an arrow. The vane is fixed to a vertical shaft of radius and ass 2.07 kg that is free to turn in its roof ount as shown in the figure. The student sets up an experient to easure the rotational inertia of the rooster and arrow. String wound about the shaft passes over a pulley and is connected to a 3.8 kg ass hanging over the edge of the roof. When the 3.8 kg ass is released, the student deterines the tie t that the ass takes to fall through a distance 0.6. The acceleration of gravity is 9.8 /s 2. 2r ind the rotational inertia I of the rooster and arrow, if t 16.6 s. Correct answer: kg 2. Airplane oentu 013 (part 1 of 2) 10.0 points An airplane of ass 1582 kg flies level to the ground at an altitude of 12 k with a constant speed of 16 /s relative to the Earth. What is the agnitude of the airplane s angular oentu relative to a ground observer directly below the airplane in kg 2 /s? Correct answer: kg 2 /s. 01 (part 2 of 2) 10.0 points Does this value change as the airplane continues its otion along a straight line? h 1. Yes. L changes with certain period as the airplane oves. 2. Yes. L increases as the airplane oves. 3. No. L constant. correct. Yes. L decreases as the airplane oves. 5. Yes. L changes in a rando pattern as the airplane oves. Asteroid Collision 015 (part 1 of 3) 10.0 points Consider an Earth-like planet hit by an asteroid. The planet has ass p kg and radius R p , and you ay approxiate it as a solid ball of unifor density. It rotates on its axis once every T 11 hr. The asteroid has ass a kg and speed v a /s (relative to the planet s center); its velocity vector points θ 33 below the Eastward horizontal. The ipact happens at an equatorial location. The picture below shows the view fro above the planet s North pole: ω v irst, calculate the planet s angular oentu (relative to its spin axis) before the ipact. Correct answer: kg 2 /s. 016 (part 2 of 3) 10.0 points Calculate the asteroid s angular oentu relative to the planetary axis. Correct answer: kg 2 /s. R θ
4 Version PREVIEW Torque Chap. 8 sizeore (13756) 017 (part 3 of 3) 10.0 points The ipact is totally inelastic the asteroid is stuck in the planet s crust. But thanks to the asteroid s angular oentu, the planet rotates faster after the ipact than it did before. By how any seconds has the collision shortened the planetary day? or siplicity, ignore the effect of the asteroid s ass on the planet s oent of inertia and assue I after I before planet. Warning: At interediate stages of this calculation, do not round off interediate results and keep at least 7 significant digits. Correct answer: s. Ball lying Off Slide points A child takes a ball and places it at the top of a slide, at an initial height. The ball starts fro rest, rolls without slipping down the slide and flies off the end into the air, with an initial angle of 32. Ignore loss to friction and air resistance. Which stateents are true throughout the ball s otion? I. Angular oentu of the ball ust be conserved. II. Linear oentu of the ball ust be conserved. III. echanical energy of the ball ust be conserved. IV. The ball will keep traveling upward until it reaches its initial height. V. The ball will travel up to a axiu height less than its initial height. 1. I, II, III and V only 2. I, II and IV only 3. II and IV only. II, III and V only 5. III and V only correct 6. I and IV only 7. II and V only 8. I, II, III and IV only 9. I and V only 10. III and IV only Bicycle Down a Hill 019 (part 1 of 3) 10.0 points A bicycle wheel of radius 0.32 rolls down a hill without slipping. Its linear velocity increases constantly fro 0 to 7 /s in 3. s. What is its angular acceleration? Correct answer: rad/s (part 2 of 3) 10.0 points Through what angle does the wheel turn in the 3. s? Correct answer: rad. 021 (part 3 of 3) 10.0 points How any revolutions does it ake? Correct answer: rev. Bohr odel of Hydrogen (part 1 of 2) 10.0 points In the Bohr s odel of the hydrogen ato, the electron oves in a circular orbit of radius around the proton. Assue that the orbital angular oentu of the electron is equal to h. Calculate the orbital speed of the electron. Correct answer: /s. 023 (part 2 of 2) 10.0 points Calculate the angular frequency of the electron s otion Correct answer: s 1. Bullet Hits a Cube points
5 Version PREVIEW Torque Chap. 8 sizeore (13756) 5 Assue: A bullet of ass and cube of ass undergo an inelastic collision, where. Note: The oent of inertia of this cube (with edges of length 2 a and ass ) about an axis along one of its edges is 8 a2. 3 A solid cube is resting on a horizontal surface. The cube is constrained to rotate about an axis at its botto left edge (due to a sall obstacle on the table). A bullet with speed v in is shot at the left-hand face at a height of a. The bullet gets ebedded in the cube. 3 ω 2 a 3 a v in g ind the iniu value of v in required to tip the cube so that it falls its right-hand face. 1. v in ( ) 5 g a v in ( ) 3 g a v in ( ) 2 g a 2 1. v in ( ) 3 g a 2 1 correct 5. v in ( ) 3 g a 5 1 Bullet Rotates a Rod (part 1 of 2) 10.0 points A wooden block of ass hangs fro a rigid rod of length l having negligible ass. The rod is pivoted at its upper end. A bullet of ass traveling horizontally and noral to the rod with speed v hits the block and gets ebedded in it. v What is the angular oentu L of the block-bullet syste, with respect to the pivot point iediately after the collision? 1. L ( ) v l ( ) 2. L v l + 3. L v l. L ( + ) v l 5. L v l correct 026 (part 2 of 2) 10.0 points What is the fraction K f (the final kinetic energy copared to the initial kinetic energy) in the collision? 1. K f 2. K f 3. K f. K f 5. K f + + correct 2 + Bullet Rotates a Rod (part 1 of 2) 10.0 points A wooden block of ass hangs fro a rigid rod of length l having negligible ass. The rod is pivoted at its upper end. A bullet of ass traveling horizontally and noral to the rod with speed v hits the block and gets ebedded in it. l
6 Version PREVIEW Torque Chap. 8 sizeore (13756) 6 erry-go-round? v What is the angular oentu L of the block-bullet syste, with respect to the pivot point iediately after the collision? 1. L ( ) v l ( ) 2. L v l + 3. L v l correct. L v l 5. L ( + ) v l 028 (part 2 of 2) 10.0 points What is the fraction K f (the final kinetic energy copared to the initial kinetic energy) in the collision? 1. K f 2. K f 3. K f. K f 5. K f + + correct 2 + Child on a errygoround points A playground erry-go-round of radius 2.3 has a oent of inertia 292 kg. 2 and is rotating at 15 rev/in about a frictionless vertical axle. acing the axle, a 33 kg child hops onto the erry-go-round, and anages to sit down on the edge. What is the new angular speed of the l Correct answer: rev/in. Disk and Hoop Race 030 (part 1 of 2) 10.0 points A unifor solid disk and a unifor hoop are placed side by side at the top of an incline of height h. If they are released fro rest and roll without slipping, deterine their speeds when they reach the botto. (d disk, h hoop) 2 1. v d 3 h g, v h 3 h g 2. v d 3 h g, v h h g correct 3. v d 2 h g, v h h g. v d h g, v h 2 h g 1 5. v d 2 h g, 1 v h 3 h g 031 (part 2 of 2) 10.0 points Which object reaches the botto first? 1. both at the sae tie 2. the hoop 3. the disk correct Dropped Coin points A coin with a diaeter of 2.9 c is dropped onto a horizontal surface. The coin starts out with an initial angular speed of 1.7 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular deceleration of agnitude 1.66 rad/s 2, How far does the coin roll before coing to rest? Correct answer: Dropped Rod 033 (part 1 of 2) 10.0 points
7 Version PREVIEW Torque Chap. 8 sizeore (13756) 7 A thin rod of length 2.3 and ass 2.3 kg is held vertically with its lower end resting on a frictionless horizontal surface. The rod is then let go to fall freely. The acceleration of gravity is 9.8 /s 2. Deterine the speed of its center of ass just before it hits horizontal surface. Correct answer: /s. 03 (part 2 of 2) 10.0 points Suppose the rod were pivoted at its lower end. Deterine the speed of the rod s center of ass just before it hits the surface. Correct answer: igure Skater 035 (part 1 of 2) 10.0 points A figure skater rotating on one spot with both ars and one leg extended has oent of inertia I i. She then pulls in her ars and the extended leg, reducing her oent of inertia to 0.75 I i. What is the ratio of her final to initial kinetic energy? 1. 1/ /9 5. 9/ /3 7. 3/8 8. /3 correct 9. 3/ II. echanical energy was conserved. III. The kinetic energy changed because of energy dissipation due to friction. IV. Her rotation rate changed in response to a torque exerted by pulling in her ars and leg. Which is the correct cobination of stateents? 1. II 2. I, II, IV 3. I and II. I correct 5. I, II, III Hands on Big Ben 037 (part 1 of 2) 10.0 points The hour and inute hands of Big Ben in London are 2.79 and.6 long and have asses of 60.6 kg and 108 kg respectively. Calculate the total angular oentu of the inute hand about the center point. Treat the hand as long, thin rod. Treat into the clock as the positive direction. Correct answer: kg 2 /s. 038 (part 2 of 2) 10.0 points Calculate the total angular oentu of the hour hand about the center point. Treat the hand as long, thin rod, and into the clock as the positive direction. Correct answer: kg 2 /s. Lawn Roller 039 (part 1 of 2) 10.0 points A constant horizontal force of 20 N is applied to a lawn roller in the for of a unifor solid cylinder of radius 0.5 and ass 12 kg. 036 (part 2 of 2) 10.0 points Consider the following stateents for the figure skater: I. Angular oentu was conserved.
8 Version PREVIEW Torque Chap. 8 sizeore (13756) 8 R If the roller rolls without slipping, find the acceleration of the center of ass. The acceleration of gravity is 9.8 /s L f L i Spinning lywheel in a Suitcase points A suitcase containing a spinning flywheel is rotated about the vertical axis as shown in (a). As it rotates, the botto of the suitcase oves out and up, as in (b). Correct answer: /s (part 2 of 2) 10.0 points ind the iniu coefficient of friction necessary to prevent slipping. Correct answer: ouse on Turntable points A ouse hangs on the ri of a spinning turntable. The rotational inertia of the ouse about the center of the turntable is about the sae as the rotational inertia of the turntable by itself. ouse and turntable are freely spinning with constant angular velocity ω. The ouse starts to crawl toward the center of the turntable. At a particular position the angular velocity of ouse and turntable has increased to ω. Before After (a) (b) ro this, we can conclude that the flywheel as seen fro the side of the suitcase as in (a), rotates 1. clockwise correct 2. counterclockwise before rotation after rotation Wrench Orientations points You are using a wrench to tighten a nut. ω ω At this instant, what is the total angular oentu of the syste in ters of its original value L i? 1. L f L i correct 2. L f L i 3. L f 16L i. L f L i 16
9 Version PREVIEW Torque Chap. 8 sizeore (13756) 9 rod wrench wrench nut 1 nut 2 rod wrench wrench nut 3 nut Which of the following correctly lists the arrangeents (above) in descending order of torque agnitude? 1. τ 1 τ 2 τ 3 τ 2. τ 2 τ τ 1 τ 3 3. τ 2 τ 1 τ τ 3 correct. τ 1 τ 3 τ 2 τ 5. τ 3 τ 2 τ τ 1 6. τ 2 τ τ 3 τ 1 7. τ 3 τ τ 2 τ 1 8. τ 2 τ 1 τ 3 τ 9. τ τ 2 τ 3 τ τ 3 τ 1 τ 2 τ
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