AP Physics 1 Lesson 16 Homework Newton s First and Second Law of Rotational Motion Outcomes Define rotational inertia, torque, and center of gravity. State and explain Newton s first Law of Motion as it relates to rotational motion. Establish criteria for rotational equilibrium and apply them to unique situations. Determine the net torque on a system and discover its relationship to rotational inertia and acceleration. Produce torque-angular acceleration graphs and determine rotational inertia experimentally. Name Date Period Questions 1 and 2 refer to the following material: An ant of mass m clings to the rim of a flywheel of radius r, as shown in the figure. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity ω. As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight. 1. 2. It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points? A) I B) II C) III D) IV What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point III? A) mg B) mω 2 r C) mω 2 r mg D) mω 2 r+mg 3. 1
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Use the scenario below to answer questions 6. and 7. 6. 7. What is the tension in the left chain? A) 250 N B) 375 N C) 500 N D) 625 N How far from the left end of the board is the person sitting? A) 0.4 m B) 1.5 m C) 2 m D) 2.5 m 8. 9. A) A B) B C) C D) D A stunt woman is jumping several cars with a motorcycle. While the rider and the motorcycle are in the air, she uses the throttle to cause the rear wheel to spin faster. What happens to the ridermotorcycle system when the rear wheel spins faster? A) The front of the motorcycle rotates upward. B) The rear of the motorcycle rotates upward. C) The rider-motorcycle system does not rotate. D) The rider-motorcycle system rotates to the left. 10. A) 1.5 kg B) 2 kg C) 3 kg D) 6 kg 3
11. A bowling ball is thrown down the bowling lane so that it is initially spinning with backspin and sliding forward at the same time. As it moves, how does the force of friction affect the ball s spin rate and the speed of the ball s center of mass? Spin Rate Speed of Center of Mass A) Spins faster Decreases B) Spins faster Increases C) No change No change D) Spins slower Decreases 12. 13. In which of the following diagrams is the torque about point O equal in magnitude to the torque about point X in the diagram above? (All forces lie in the plane of the paper.) 4
14. 15. A solid sphere has a mass of M and a radius of R. Which of the following statements are true about the sphere s rotational inertia? Select two answers. A) Rotational inertia depends on the choice of the axis of rotation. B) Rotational inertia is proportional to the sphere s mass regardless of the choice of the axis of rotation. C) Rotational inertia is inversely proportional to the sphere s speed. D) Rotational inertia has the units of kg m/s 2. 16. 5
17. A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown above. The magnitude of the net torque on the system about the axis is a. zero b. FR c. 2FR d. 5FR e. 14FR 18. For the wheel-and-axle system shown at the right, which of the following expresses the condition required for the system to be in static equilibrium? a. m 1 = m 2 b. am 1 = bm 2 c. am 2 = bm 1 d. a 2 m l = b 2 m 2 e. b 2 m 1 = a 2 m 2 19. 20. A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed ω of the wheel is increased from zero to ω f in a time interval T. What is the average net torque on the wheel during this time interval? a. b. c. d. e. A uniform stick has length L. The moment of inertia about the center of the stick is I o. A particle of mass M is attached to one end of the stick. The moment of inertia of the combined system about the center of the stick is Iω T f (A) (B) (C) (D) (E) 6
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Free Response 1. Use g = 10 m/s 2. The apparatus above was used in an experiment and the following data was gathered: Hanging mass = 0.500 kg Radius of spool string is wound around = 0.030 meters Average time for apparatus to make 5 revolutions, starting from rest = 3.96 seconds The small pulley is frictionless and massless. a) Find the angular acceleration of the rotating apparatus. b) Find the linear acceleration of the hanging mass. c) Find the Tension in the string. d) Find the total rotational inertia of the apparatus. The black disc of radius 10.0 cm (with the appropriate sized hole in the middle) under the table is now placed on top of the white disc and the experiment is repeated. After analysis of the new data, it is determined the total rotational inertia of this new system is 0.057 kg * m 2. e) If the black disc is of constant density throughout, and the hole in the middle can be neglected, what is the mass of the black disc? 10
2. A uniform solid cylinder of mass m 1 and radius R is mounted on frictionless bearings about a fixed axis through O. The moment of inertia of the cylinder about the axis is I = ½m 1 R 2. A block of mass m 2, suspended by a cord wrapped around the cylinder as shown above, is released at time t = 0. a. On the diagram below draw and identify all of the forces acting on the cylinder and on the block. b. In terms of m l, m 2, R. and g, determine each of the following. i. The acceleration of the block ii. The tension in the cord 11
3. Note: Figure not drawn to scale. 2013. A disk of mass M = 2.0 kg and radius R = 0.10 m is supported by a rope of negligible mass, as shown above. The rope is attached to the ceiling at one end and passes under the disk. The other end of the rope is pulled upward with a force F A. The rotational inertia of the disk around its center is MR 2 /2. (a) (i) Calculate the magnitude of the force F A necessary to hold the disk at rest. (ii) If the disk had been a hoop of the same mass and radius, how would your answer to (a)(i) change? Justify your answer in words. At time t = 0, the force F A is increased to 12 N, causing the disk to accelerate upward. The rope does not slip on the disk as the disk rotates. (b) (i) Calculate the linear acceleration of the disk. (ii) If the disk had been a hoop of the same mass and radius, how would your answer to (b)(i) change? Justify your answer in words. 12
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