Question

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that

Group of answer choices

the rotational inertia of the system increases and the rotational speed decreases.

the rotational inertia of the system decreases and the rotational speed increases.

the rotational inertia of the system decreases and the rotational speed remains the same.

the rotational inertia of the system increases and the rotational speed increases.

the rotational inertia of the system decreases and the rotational speed decreases.

Answer 1

Here let the moment of inertia of the merry go round be,

(ie, remains constant,where M is mass of the merry go round disc and R is the radius of the merry go round)

Also since a person Diego be at a distance r from the centre of the rotational axis initially,

So,The moment of inertia of the person,

Where m is the mass of person Diego.

So,The moment of inertia of the system of merry go round and Diego,

If the person Diego walks from the a radius to the centre of the circle(Axis of rotation),

The final distance of the person from the axis of rotation,

So,The final moment of inertia of the combned system,

Let the initial angular velocity of rotation of the system be,

And the final angular velocity of the rotation of the system,

Here since there is no net external force on the system,we have the angular momentum of the system is conserved.

The inital angular momentum pf the system,

Final angular momentum of the system,

So,

ie,

So,Final angular velocity of the system,

So,The final angular velocity is greater than the initial angular velocity of the system.

ie,

Also the initial moment of inertia of the system,

Final moment of inertia of the system,

So,The final moment of inertia of system is less than the initial moment of inertia of the system.

ie,

So,Rotational inertia of the system decreases and the rotatonal speed increases.