A merry-go-round with a moment of inertia equal to 1260 kg·m^2 and a radius of 2.5 m rotates wit

step 1 We want to find the mass of the child. We know that the moments of inertia of the merry -go -rou

A merry-go-round with a moment of inertia equal to 1260...

A merry-go-round with a moment of inertia equal to $1260 kg\cdot m^2$ and a radius of 2.5 m rotates with negligible friction at 1.70 rad/s. A child initially standing still next to the merry-go-round jumps onto the edge of the platform straight toward the axis of rotation, causing the platform to slow to 1.35 rad/s. What is her mass?

Key Concepts

Conservation of Angular Momentum

This principle states that if no net external torque acts on a system, the total angular momentum remains constant. In rotational dynamics problems like this, even when additional mass is added, the product of the moment of inertia and the angular velocity does not change, allowing us to solve for unknown parameters by equating initial and final angular momenta.

Moment of Inertia

The moment of inertia is a measure of how mass is distributed with respect to the axis of rotation and quantifies an object's resistance to changes in its rotational motion. When masses are added or repositioned in a rotating system, the overall moment of inertia changes, which in turn affects the angular velocity if angular momentum is conserved.

Angular Velocity

Angular velocity is the rate at which an object rotates, measured in radians per second. In problems concerning rotational dynamics, changes in angular velocity often result from modifications to the system’s moment of inertia, especially when no external torques are acting.

Rotational Collisions

In scenarios where objects join a rotating system, such as a person jumping onto a platform, the event is akin to an inelastic collision in rotational dynamics. Although kinetic energy may not be conserved in such interactions, angular momentum is conserved, making it possible to relate the system’s initial and final states.

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