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*m2) 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 τ = 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 child (m = 25 kg) is riding on a frictionless merry-go-round at 1.5 m from the center axle. The merry-go-round (Imgr = 1000 kg*m2) is traveling at an angular velocity of 2 rad/s. (Hint: Watch the following videos: "Session 9/Lecture/Rotational Motion Example Problems/HW Problem 1 F-H Hints")
Question for thought: 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")
Question for thought: 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*m2. For this problem, all answers involving a rotational component will be expressed in revolutions rather than radians. (Hint: Watch the following videos: "Session 9/Lecture/Rotational Motion Example Problems/Conservation of Angular Momentum HW Problem Hints")
Question for thought: (3F) What is the source of the torque that accelerates the student-wheel-stool system?
Concept Question
1. The torque due to a force F acting tangentially at a distance r from the center is given by,
Lets say that the applied force is rotating the merry go round in counter clockwise direction and the torque is positive.
(a) Substituting values we get,
(b) The direction of torque vector is vertically upwards (counter clockwise motion) hence it is positive.
(c) Substituting values we get,
(d) Here this is friction hence the torque vector is vertically downwards (friction tries to rotate in clockwise motion) hence it is negative.
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