Answer :
Final answer:
The interaction of a person with the disk-shaped merry-go-round will effectively change the moment of inertia of the system, thereby affecting the angular speed of the merry-go-round. The tangential speed at any point on the merry-go-round increases with its distance from the axis of rotation.
Explanation:
When considering a merry-go-round or any rotating object, the concepts of angular acceleration and moment of inertia come into play. In this instance, a disk-shaped merry-go-round of radius 2.73 m and mass 145 kg is rotating freely with an angular speed of 0.651 rev/s. When a person comes in contact with it, according to the conservation of angular momentum, the moment of inertia of the system increases, resulting in a decrease in angular velocity.
More specifically, if we consider the person to be a point mass at some distance, we can calculate the new moment of inertia of the system - which would factor in the person's mass and the square of the distance. This would be Ic = MR² = (person's mass)(distance)², and the sum of this value and the original moment of inertia of the merry-go-round will give us the total moment of inertia of the system.
This is crucial because the magnitude of the angular acceleration directly depends on the moment of inertia - a greater moment of inertia would result in a lesser angular acceleration, and vice versa. Also, the tangential speed of any point on the merry-go-round would be the product of the angular speed and its distance from the axis of rotation, meaning it increases with distance for a constant angular velocity.
Learn more about Angular Momentum and Moment of Inertia here:
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