Suppose the platform with the kid in the previous problem is rotating in an anticlockwise direction at an angular speed [tex]\omega[/tex]. The kid starts walking along the rim with a speed [tex]v[/tex] relative to the platform, also in the anticlockwise direction. Find the new angular speed of the platform.

Question

03-04-2025
Physics

High School

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Suppose the platform with the kid in the previous problem is rotating in an anticlockwise direction at an angular speed [tex]\omega[/tex]. The kid starts walking along the rim with a speed [tex]v[/tex] relative to the platform, also in the anticlockwise direction. Find the new angular speed of the platform.

Answer :

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Final answer:

When a child walks along the rim of a rotating platform in the anticlockwise direction, the angular momentum of the system increases, resulting in an increase in the platform's new angular speed.

Explanation:

When a child walks along the rim of a rotating platform in the anticlockwise direction, the angular momentum of the system increases. As a result, the platform's new angular speed will also increase.

Let's consider the initial and final angular momentums:

Initial angular momentum = (Mass of platform * Initial angular velocity) + (Mass of child * Initial angular velocity)

Final angular momentum = (Mass of platform * Final angular velocity) + (Mass of child * Final angular velocity)

Since the angular momentum is conserved, the initial angular momentum is equal to the final angular momentum:

(Mass of platform * Initial angular velocity) + (Mass of child * Initial angular velocity) = (Mass of platform * Final angular velocity) + (Mass of child * Final angular velocity)

You can solve this equation to find the new angular velocity of the platform.