(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.
(a)
Answer to Problem 3SP
The rotational inertia of the children is
Explanation of Solution
Given info: The total mass of the children is
Write the expression for the rotational inertia of the children.
Here,
Substitute
Write the expression for total rotational inertia acting on the merry-go-round by adding the new rotational inertia of the children with the rotational inertia of the merry-go-round.
Here,
Substitute
Conclusion:
Therefore, the rotational inertia of the children is
(b)
The new rotational inertia of the merry-go-round.
(b)
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
Write the expression for total rotational inertia acting on the merry-go-round by adding the new rotational inertia of the children with the rotational inertia of the merry-go-round.
Here,
Substitute
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.
(c)
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
Here,
Substitute
Conclusion:
Therefore, The rotational velocity of the merry-go-round after the children move towards the center is
(d)
Whether the merry-go-round rotationally accelerated during the process and where does the accelerating torque come from.
(d)
Answer to Problem 3SP
Yes, the merry-go-round is rotationally accelerated during the process
Explanation of Solution
The rotational acceleration is defined as the ratio of torque and rotational inertia. The main causes of rotational acceleration is friction.
Write the expression for the rotational acceleration.
Here,
When the children are 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 is rotationally accelerated during the process
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