A student sitting on a stool that is free to rotate, but is initially at rest, holds a bicycle wheel. The wheel has a rotational velocity of 8 rev/s about a vertical axis, as shown in the SP4 diagram. The rotational inertia of the wheel is 2.5 kg·m2 about its center, and the rotational inertia of the student and wheel and stool about the rotational axis of the stool is 6 kg·m2.
- a. What is the rotational velocity of the wheel in rad/s?
- b. What are the magnitude and direction of the initial
angular momentum of the system? - c. If the student flips the axis of the wheel, reversing the direction of its angular-momentum vector, what is the rotational velocity (magnitude and direction) of the student and the stool about their axis after the wheel is flipped? (Hint: See fig. 8.24.)
- d. Where does the torque come from that accelerates the student and the stool? Explain.
(a)
The rotational velocity of the wheel in
Answer to Problem 4SP
The rotational velocity of the wheel is
Explanation of Solution
Given info: The rotational velocity is
Write the expression for conversion relation connecting
Convert
Conclusion:
Therefore, the rotational velocity of the wheel is
(b)
The magnitude and the direction of the initial angular momentum of the system.
Answer to Problem 4SP
The angular momentum of the system is
Explanation of Solution
Write the expression for the angular momentum.
Here,
Substitute
Conclusion:
Therefore, the angular momentum of the system is
(c)
The rotational velocity of the student and the stool about their axis after the wheel is flipped.
Answer to Problem 4SP
The rotational velocity of the student and the stool about their axis is
Explanation of Solution
From the conservation of angular momentum, the angular velocity of the student and the stool is,
Here,
Rewrite the relation of the angular momentum then rearrange it for the rotational velocity of the student and the stool.
Rewrite the relation for the rotational velocity of the student and the stool.
Substitute
The direction of the rotational velocity of the student and the stool would be the direction of initial rotational velocity direction of the wheel.
Conclusion:
Therefore, the rotational velocity of the student and the stool about their axis is
(d)
Where will be the torque come from that accelerates the student and the stool.
Answer to Problem 4SP
The student exerts forces on the handles when he flips the wheel.
Explanation of Solution
For the flip of the wheel, the student exerts a certain amount force which creates the torque on the wheel then this torque produce the equal amount of opposite torque on the student and the stool. This happens for the system to be conserved.
Conclusion:
Therefore, the student exerts forces on the handles when he flips the wheel.
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