In the park, several children (having a total mass of 90 kg) are riding on a merry-go-round that has a rotational inertia of 1100 kg·m2 and a radius of 2.4 m. The average distance of the children from the axle of the merry-go-round is 2.2 m initially, because they are all riding near the edge.
- a. 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?
- b. The children now move inward toward the center of the merry-go-round so that their average distance from the axle is 0.8 m. What is the new rotational inertia for the system?
- c. If the initial rotational velocity of the merry-go-round was 1.3 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 .) - d. Is the merry-go-round rotationally accelerated during this process? If so, where does the accelerating torque come from?
(a)
The rotational inertia of the children about the axle of the merry-go-round and the total rotational inertia of the children and the merry-go-round.
Answer to Problem 3SP
The rotational inertia of the children is
Explanation of Solution
Given info: Mass is
Write the expression for the rotational inertia.
Here,
Substitute
The total rotational inertia acting on the merry-go—round is given by adding with the rotational inertia of the merry-go-round.
Conclusion:
Therefore, the rotational inertia of the children is
(b)
The new rotational inertia of the merry-go-round.
Answer to Problem 3SP
The new rotational inertia of the merry-go-round is
Explanation of Solution
Write the expression for the rotational inertia.
Substitute
The total rotational inertia acting on the merry-go—round is given by adding with the rotational inertia of the merry-go-round.
Conclusion:
Therefore, the new rotational inertia of the merry-go-round is
(c)
The rotational velocity of the merry-go-round after the children move in towards the center.
Answer to Problem 3SP
The rotational velocity of the merry-go-round after the children move towards the center is
Explanation of Solution
Write the expression for the conservation of angular momentum.
Here,
Substitute
Conclusion:
Therefore, the rotational velocity of the merry-go-round will be
(d)
Whether the merry-go-round rotationally accelerated during the process and where does the accelerating torque come from.
Answer to Problem 3SP
Yes, the merry-go-round rotationally accelerated during the process
Explanation of Solution
Write the expression for the rotational acceleration.
When the children moving, at that time the friction between the feet of the children and the merry-go-round produces an accelerating torque.
Conclusion:
Therefore, the merry-go-round rotationally accelerated during the process
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Chapter 8 Solutions
Physics of Everyday Phenomena
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