For the remaining problem parts, you may ignore friction. (Hint: Watch the follo

Question

For the remaining problem parts, you may ignore friction. (Hint: Watch the following videos: "Session 9/Lecture/Rotational Motion Example Problems/HW Problem 1 F-H Hints")

A child pushes her friend (m = 25 kg) located at a radius r = 1.5 m on a merry-go-round (rmgr = 2.0 m, Imgr = 1000 kg*m^2) with a constant force F = 90 N applied tangentially to the edge of the merry-go-round (i.e., the force is perpendicular to the radius). The merry-go-round resists spinning with a frictional force of f = 10 N acting at a radius of 1 m and a frictional torque ? = 15 N*m acting at the axle of the merry-go-round, and the merry-go-round is initially at rest. (Hint: Watch the following videos: Session 9/Lecture/Rotational Motion Example Problems/Net Torque Example Problem 3)A: Where is the center of mass located in the plank? B: What is the magnitude of the torque of the plank about the edge of the dock? C: How far from the edge of the dock can the boy walk on the plank before the plank starts tipping into water? D: How could the boy test this conclusion without taking the risk of falling in the water? A person sits on a frictionless stool that is free to rotate but is initially at rest. The person is holding a bicycle wheel (I = 3 kg*m2) that is rotating at 8 rev/s in the clockwise direction as viewed from above, and the moment of inertia of the person-wheel-stool system is 9 kg*m^2. (Hint: Watch the following videos: Session 9/Lecture/Rotational Motion Example Problems/Conservation of Angular Momentum HW Problem Hints)A: What is magnitude of the angular momentum of the system? B: What is direction of the angular momentum of the system? C: The person flips the rotating wheel over 180 degrees, taking 0.5 seconds to complete this action. What is the magnitude of the rotational velocity of the person-wheel-stool system about the axis of the stool after the wheel is flipped? D: What is the direction of the rotational velocity of the person-wheel-stool system about the axis of the stool after the wheel is flipped? E: What is the magnitude of the rotational acceleration of the person-wheel-stool system? F: What is the source of the torque that accelerates the student-wheel-stool system? A: What is the magnitude of the net torque acting on the merry-go-round about its axle? B: What is moment of inertia of the merry-go-round with the child on it? C: What is the magnitude of the rotational acceleration of the merry-go-round? D: If the child pushes for 15 s, what is the magnitude of rotational velocity of the merry-go-round at 15 s? E: Once the child stops pushing at 15 s, how long does it take for the merry-go-round to come to a stop? For the remaining problem parts, you may ignore friction. (Hint: Watch the following videos: Session 9/Lecture/Rotational Motion Example Problems/HW Problem 1 F-H Hints) F: If the merry-go-round were traveling at a rotational velocity of 2 rad/s and the child riding on the merry-go-round moves from a radius of 1.5 m outward to a radius of 2.0 m in 1 second, what is the magnitude of the rotational velocity of the merry-go-round immediately after the child moves? G: In the process of the child moving outward, what is the magnitude of the rotational acceleration of the merry-go-round? H: In the process of the child moving outward, is there a torque accelerating the system? If yes, what is the source of the accelerating torque? A child (m = 25 kg) walks along a 4 m plank of uniform density (m = 8 kg) that is laying with one end extending 1 m off the end of a dock (i.e., 3 m of the plank are on the dock, and 1 m of the plank extends off the dock). (Hint: Watch the following videos: Session 9/Lecture/Lesson on Rotational Motion/Center of Mass and Session 9/Lecture/Rotational Motion Example Problems/Net Torque Example Problem 1 and Session 9/Lecture/Rotational Motion Example Problems/Net Torque Example Problem 2)

Explanation / Answer

1)
Net torque = 90*1.5 = 135

I = (1000 + 25*1.5*1.5) of merry go round and child

T = Ialpha

alpha = 0.127 rad/sec^2

w = alpha*t = 1.917 rad/sec

e)time to take stop

10*1 = -(1000 + 25*1.5*1.5)*alpha1
alpha1 = decelration causing = 0.00946 rad/sec^2

t = 202.34 sec

f)(1000 + 25*1.5*1.5)*2 = (1000+ 25*2*2)*w
1056.25*2 = 1100*w

w = 1.92 rad/sec

g) 1.92/1 = 1.92 rad/s^2

h)
source is child moving towards out , its not torque sicne no external troque momentum conserves
for the system
wat ever torque it is inside system of child and merry go round

3)
when he hold wheel both chair and all are rotating with 8rev/sec =50.26 rad/sec
3 *50.26 = 9*w
w = 16.75 rad/sec
momentum aftr holding = 3 *50.26 = 150.78

b)
downawards
c)
150.78 = - 3*16.75 + 6*w

w = 33.505 rad/sec

d) clockwise

e) 67.01

f)
its inside of system torque not external torque

c)

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