A child is sitting on a merry-go-round that is spinning. If the child moves towards the center, what happens to the angular velocity of the merry-go-round?
Practice Questions
1 question
Q1
A child is sitting on a merry-go-round that is spinning. If the child moves towards the center, what happens to the angular velocity of the merry-go-round?
Increases
Decreases
Remains the same
Becomes zero
As the child moves towards the center, the moment of inertia decreases, and to conserve angular momentum, the angular velocity must increase.
Questions & Step-by-step Solutions
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Q
Q: A child is sitting on a merry-go-round that is spinning. If the child moves towards the center, what happens to the angular velocity of the merry-go-round?
Solution: As the child moves towards the center, the moment of inertia decreases, and to conserve angular momentum, the angular velocity must increase.
Steps: 6
Step 1: Understand that the merry-go-round is spinning and has a certain speed called angular velocity.
Step 2: Know that the child sitting on the merry-go-round has mass and contributes to the overall mass distribution, which is called moment of inertia.
Step 3: When the child moves towards the center, they are reducing the distance from the center of the merry-go-round.
Step 4: Realize that moving towards the center decreases the moment of inertia because the mass is closer to the axis of rotation.
Step 5: Remember the principle of conservation of angular momentum, which states that if no external forces act on the system, the total angular momentum remains constant.
Step 6: Since the moment of inertia decreases when the child moves towards the center, the angular velocity must increase to keep the angular momentum constant.
