1. A merry go round in the park has a radius of 1.8 m and a rotational inertia of 900kg-m2.1
A child pushes the merry-go-round with a constant force of 80 n applied at the edge and parallel to the ege.
A-frictional torque of 12 N-m acts at the axle of the merry-go-around.
1. What is the rotational acceleration of the merry-go-round?
2. What is the net torque acting on the merry-go-round about its axle?
3. At this rate, what will the rotational velocity of the merry-go-round be after 15 s if it starts from rest?
4. What is the rotational acceleration of the merry-go p around if the child stops pushing after 15 s? How long will it take for the merry-go-round to stop turning?
2. A4-m long plank with a weight of 80 N is placed on a dock with 1m of its length extended over the water, as in the diagram. The plank is uniform in density so that the center of gravity of the plank is located at the center of the plank. A boy with a weight og 150 N is standing on the plank and moving out slowly form the edge of dock.
1. What is the torque exerted with the weight of the plank about the pivot point at the edge of the dock? (treat all the weight as acting during the center go gravity of the plank)
2. How far from the edge f the dock can the boy move until the plank is now on the verge of tipping?
3. How can the boy test this conclusion without falling in the water? Describe
3. In the park several children with a total mass of 240 kg are riding on a merry-go-round that a rotational inertia of 1500 kg-m2 and a radius f 2.2 m. The average distance of the children from the axle of the merry-go-round is 2.0m initially, since the t are all riding near the edge.
1. What is the rotational inertia of the children about the axle of the merry-go-round? What is the total rotational inertia of the children and the merry-go-round?
2. The children now move inward toward the center of the merry-go-round so that their average distance from the axle is 0.5 m. what is the new rotational inertia for the system?
3. If the initial rotational velocity of the merry-go-round was 1.2 rad/s, what is the rotational velocity after the children move in toward the center, assuming that the frictional torque can be ignored? (Use conservation of angular momentum.)
4. Is the merry-go-round rotationally accelerated during this process? If so, where does the accelerating torque come from?
4. A student sitting on a stool that is free to rotate however is initially at rest, holds a bicycle wheel. The wheel has a rotational velocity of 5 rev/s about a vertical axis, as shown in the diagram. The rotational inertia of the wheel is 2kg-m2 about its center and the rotational axis inertia of the student and well and platform about of the rotational axis of the plat form is 6 kg-m2.
1. What are the magnitude and direction of the initial angular momentum of the system?
2. If the student flips the axis of the wheel, reversing the direction of its angular-momentum vector, what is the rotational velocity (direction and magnitude) of the student and the stool about their axis after the wheel is flipped?
3. Where does the torque come from that accelerate the student and the stool? Describe.