F166Chapter 8 Rotational Motion of Solid ObjectsexercisesEI Suppose that a merry-go-round is rotating at the rate of10 rev/min.a. Express this rotational velocity in rev/s.b. Express this rotational velocity in rad/s.E2 11iontime orE3. Suppose that a disk rotates through five revolutions in4 seconds.a. What is its displacement in radians in this time?b. What is its average rotational velocity in rad/s?TheRPM.round increases at aES. A bicycle wheel is rotationally accelerated at the constantrate of 1.2 rev/s².24 cma. If it starts from rest, what is its rotational velocity after 4 s?b. Through how many revolutions does it turn in this time?E6. Tacceleration of the disk?E7. Starting from rest, a merry-go-round accelerates at a con-stant rate of 0.2 rev/s².a. What is its rotational velocity after 5 s?b. How many revolutions occur during this time?E8.A force of 50 Nic applied at the end of a wranch handle that50 Nalf-E8 DiagramE9. A weight of 30 N is located a distance of 10 cm from thefulcrum of a simple balance beam. At what distance fromthe fulcrum should a weight of 20 N be placed on the oppo-site side in order to balance the system?ElEII. Two forces are applied to a merry-go-round with a radiusof 1.2 m as shown in the diagram below. One force hasmagnitude of 80 N and the other a magnitude of 50 N.a. What is the torque about the axle of the merry-go-rounddue to the 80-N force?b. What is the torque about the axle due to the 50-N force?c. What is the net torque acting on the merry-go-round?E12.E1.2 m50 NO0.2 kgE11 DiagramE13. A wheel with a rotational inertia of 5.6 kg-m² acceleratesat a rate of 3.0 rad/s². What net torque is needed to producethis acceleration?80 NAxisWE-el?incluE15. Two 0.2-kg masses are located at either end of a 1-m long.very light and rigid rod as in the diagram. What is the rotational inertia of this system about an axis through the centerof the rod?1mE15 Diagram0.2 kgVs E16its opprettecon or use system!E17. A uniform disk with a mass of 4 kg and a radius of 0.3 m isrotating with a rotational velocity of 20 rad/sa. What is the rotational inertia of the disk? (See fig. 8.15.)b. What is the angular momentum of the disk?SP2synthesis problemsSPI. A merry-go-round in the park has a radius of 1.8 m and arotational inertia of 900 kg-m². A child pushes the merry-go-round with a constant force of 80 N applied at the edgeand parallel to the edge. A frictional torque of 12 N-m actsat the axle of the merry-go-round.andWhat is the net torque acting on the merry-go-roundabout its axle?b. What is the rotational acceleration of the merry-go-round?c. At this rate, what will the rotational velocity of themerry-go-round be after 15 s if it starts from rest?d. What is the rotational acceleration of the merry-go-round if the child stops pushing after 15 s? How longwill it take for the merry-go-round to stop turning?offALM3 mdockhe plankTreat allvity of theboy move1m1g?on without falling inSP2 DiagramSP). In the park, several children with a total mass of 240 kg areriding on a merry-go-round that has a rotational inertia of1500 kg-m² and a radius of 2.2 m. The average distance ofthe children from the axle of the merry-go-round is 2.0 minitially, since they are all riding near the edge.E18.thintheSynthesis problems 167a. What is the rotational inertia of the children about theaxle of the merry-go-round? What is the total rotationalinertia of the children and the merry-go-round?b. The children now move inward toward the center of themerry-go-round so that their average distance from theaxle is 0.5 m. What is the new rotational inertia for thesystem?c. If the initial rotational velocity of the merry-go-roundwas 1.2 rad/s, what is the rotational velocity after thechildren move in toward the center, assuming that thefrictional torque can be ignored? (Use conservation ofangular momentum.)d. Is the merry-go-round rotationally accelerated duringthis process? If so, where does the accelerating torquecome from?SP4. A student sitting on a stool that is free to rotate, but is initiallyat rest, holds a bicycle wheel. The wheel has a rotationalvelocity of 6 rev/s about a vertical axis, as shown in the dia-gram. The rotational inertia of the wheel is 2 kg m² about itscenter and the rotational inertia of the student and wheel andstool about the rotational axis of the stool is 5 kg-m².a. What are the magnitude and direction of the initialangular momentum of the system?b. If the student flips the axis of the wheel, reversingthe direction of its angular-momentum vector, what isthe rotational velocity (magnitude and direction) of thestudent and the stool about their axis after the wheel isflipped? (Hint: See fig. 8.23.)c. Where does the torque come from that accelerates thestudent and the stool? Explain.2SP4 Diagram

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