11:26 AM Mon Oct 10 83% quest.cns.utexas.edu kolsawala (afk472) - 4-PHY317K-Homework - lang - (57345) 5 sticks to it. angular momentum with respect to the center of the merry-go-round? 1. Li = m2 v R 2. Li = m2v R 3. Li = miv 2 4. Li = mivR 5. Li = m2v 3 R Before the collision, the cylinder was not ro- 4 R tating. What is the magnitude of its angular 6. Li = miv velocity after the collision? 3 R 7. Li = miv 1. 1.4742 2. 16.4634 8. Li = m2v- 3. 25.5208 4. 28.2723 015 (part 2 of 2) 10.0 points 5. 3.91986 Consider the case where the mass of the boy is 6. 15.1141 the same as the mass of the merry-go-round; 7. 27.605 i.e., mi = m2 = m = 42 kg. The radius of 8. 6.45933 the merry-go-round is R = 13 m. The initial 9. 20.9819 velocity of the boy is v = 6 m/s. 10. 5.14038 Hint: Treat the boy and the merry-go- Answer in units of rad/s. round together as an isolated system. Determine the final angular velocity of the 014 (part 1 of 2) 10.0 points merry-go-round in radian/sec. Consider a freely spinning merry-go-round, 1. 0.17094 which can be treated as a uniform disc of ra- 2. 0.136752 dius R and mass mi rotating about a vertical 3. 0.259259 axis through its center. Initially the merry- 4. 0.205128 go-round is at rest. A boy of mass m2 jumps 5. 0.296296 with a horizontal speed v, landing at A, which 6. 0.15873 is a distance from the center. 7. 0.222222 Hint: Neglect the vertical fall of the boy. 3. 0.161616 9. 0.0888889 10. 0.355556 Answer in units of radian/sec. m2 , v R 016 (part 1 of 2) 10.0 points R/4 A spool of wire of mass 5.8 kg and radius 0.49 m is unwound under a constant wire tension 3.6 N. Assume the spool is a uniform m1 solid cylinder that rolls without slipping As the boy is approaching the merry-go- round, what is the magnitude of his initial11:25 AM Mon Oct 10 83% quest.cns.utexas.edu kolsawala (afk472) - 4-PHY317K-Homework - lang - (57345) 4 to have negligible mass and treat the masses (r and 2r) are spinning on frictionless bear- as point particles. ings at the same angular speed wo but in op- posite directions. The two disks are brought 1. 1.68 slowly together. The resulting frictional force 2. 12.528 between the surfaces eventually brings them 3. 0.945 to a common angular velocity. 4. 0.66825 5. 34.56 6. 3.67575 7. 9.537 8. 2.4 9. 13.5375 10. 8.39325 Answer in units of kg . m2. 1 10.0 points The puck in the figure has a mass of 0.103 kg. Its original distance from the center of rota- tion is 53.6 cm, and the puck is moving with What is the magnitude of that final angular a speed of 76.8 cm/s. The string is pulled velocity in terms of wo? downward 11.2 cm through the hole in the 3 frictionless table. 1 . Wf = wo 2. Wf = wo 0.103 kg 53.6 cm 3. Wf = wo 76.8 cm/s 4. Wf = WO 5 . Wf = WO CO | NCO | HN| HOT/ HOTI DOT/ NOTI COPI 6. Wf = wo What is the magnitude of the work was done on the puck? Treat the hockey puck as 7. Wf = wo a point mass. 8. Wf: Wo 1. 0.122467 9. Wf = Wo 2. 0.0544982 3. 0.0181672 013 10.0 points 4. 0.0882048 A solid cylinder of mass M = 20 kg, radius 5. 0.0111016 R = 0.15 m and uniform density is pivoted on 6. 0.0267092 a frictionless axle coaxial with its symmetry 7. 0.133211 axis. A particle of mass m = 2.9 kg and 8. 0.0991881 initial velocity vo = 14 m/s (perpendicular 9. 0.074108 to the cylinder's axis) flies too close to the 10. 0.0276887 cylinder's edge, collides with the cylinder and Answer in units of J. 2 10.0 points Two disks of identical mass but different radii11:25 AM Mon Oct 10 83% quest.cns.utexas.edu kolsawala (afk472) - 4-PHY317K-Homework - lang - (57345) 3 7. 9.00541 9. 4698 3. 5.08148 10. 1562.5 9. 4.35556 Answer in units of J. 10. 8.01818 Answer in units of N. 009 (part 2 of 2) 10.0 points Now assume the system rotates in the xy 007 (part 2 of 2) 10.0 points plane about the z axis (origin, O) with an What is the angular acceleration of the wheel? angular speed of 8 rad/s. 3 kg y 1 8 kg 1. 3.5 2. 28 3. 10.0513 4. 12.8817 5. 5.83333 - 5 m 6. 7.12727 8 rad/s 7. 2.92039 8. 6.62162 9. 13.475 4 kg - 5 m - 3 kg 10. 2.20721 Answer in units of rad/s. Find the rotational energy of the system about the z axis. 008 (part 1 of 2) 10.0 points Four particles with masses 3 kg, 4 kg, 3 kg, 1. 13671 and 8 kg are connected by rigid rods of neg- 2. 192 ligible mass as shown. Assume the system 3. 7200 rotates in the yz plane about the x axis with 4. 6300 an angular speed of 8 rad/s. 5. 1600 3 kg y 8 kg 6. 7043.75 7. 3744 8 rad/s | 8 rad/s 8. 4704 9. 6000 10. 2548 - - - - - - 8. Answer in units of J. 0 10.0 points The figure below shows a rigid system which 4 kg 5 m 3 kg can rotate, with one mass three times the other. Find the rotational energy of the system 3.1 kg 9.3 kg about the x axis. 1. 1531.25 2. 12152 1.9 m 3. 3600 4. 15876 5. 3200 What is the moment of inertia about an axis 6. 3062.5 perpendicular to the paper and through the 7. 9408 center of mass? Consider the connecting rod 8. 1584