(a)
The magnitude and the direction of the initial
(a)
Answer to Problem 4SP
The angular momentum of the system is
Explanation of Solution
Given info: The rotational velocity of the wheel is
Write the expression for the angular momentum.
Here,
Substitute
Conclusion:
Therefore, the angular momentum of the system is
(b)
The rotational velocity of the student and the stool about their axis after the wheel is flipped.
(b)
Answer to Problem 4SP
The rotational velocity of the student and the stool about their axis is
Explanation of Solution
The angular momentum gained by the student, stool, and wheel is exactly twice the original angular momentum of the wheel. The student can stop the rotation of the stool by flipping the wheel axis back to its original direction.
Write the expression for conservation of angular momentum.
Here,
Write the expression for the angular momentum of the wheel.
Here,
Substitute
Equating with the angular momentum of the wheel and the stool,
Write the expression for the angular momentum of the stool.
Here,
Substitute
Conclusion:
Therefore, the rotational velocity of the student and the stool about their axis is
(c)
Where will be the torque come from that accelerates the student and the stool.
(c)
Answer to Problem 4SP
The student exerts forces on the handles when he flips the wheel.
Explanation of Solution
The sum of the angular-momentum vector of the wheel about its axis of rotation and the angular-momentum vector of the student, stool, and wheel about the axis of rotation of the stool add to yield the original angular momentum. This will be true if the angular momentum gained by the student, stool, and wheel is exactly twice the original angular momentum of system.
The student will exert some forces on the handles to produce a torque on the wheel which then produces an equal and opposite torque on the student.
Conclusion:
Therefore, the student exerts forces on the handles when he flips the wheel.
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