A child is sitting on a merry-go-round that is spinning. If the child moves towards the center of the merry-go-round, what happens to the angular velocity of the system?
Practice Questions
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Q1
A child is sitting on a merry-go-round that is spinning. If the child moves towards the center of the merry-go-round, what happens to the angular velocity of the system?
Increases
Decreases
Remains the same
Becomes zero
As the child moves towards the center, the moment of inertia decreases, thus the angular velocity increases to conserve angular momentum.
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 of the merry-go-round, what happens to the angular velocity of the system?
Solution: As the child moves towards the center, the moment of inertia decreases, thus the angular velocity increases to conserve angular momentum.
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 a certain distance from the center, which affects the system's moment of inertia.
Step 3: Moment of inertia is a measure of how much mass is distributed away from the center. The farther the child is from the center, the higher the moment of inertia.
Step 4: When the child moves towards the center, they are reducing the distance from the center, which decreases the moment of inertia.
Step 5: Angular momentum is a property that must be conserved in a closed system. This means that if the moment of inertia decreases, the angular velocity must increase to keep the angular momentum constant.
Step 6: Therefore, as the child moves towards the center of the merry-go-round, the angular velocity of the system increases.
