A child is sitting on a merry-go-round that is spinning. If the child moves towa
Practice Questions
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
Questions & Step-by-Step Solutions
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?
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.
Angular Momentum Conservation – The principle that the total angular momentum of a closed system remains constant if no external torques act on it.
Moment of Inertia – A measure of an object's resistance to changes in its rotation, which depends on the mass distribution relative to the axis of rotation.
Angular Velocity – The rate of rotation of an object around an axis, typically measured in radians per second.
