A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a radius of 3.87m and a rotational inertia of 429kg.m^2 about the axis of rotation. A 78.4kg student walks slowly from the rim of the platform towards the center. The angular speed of the system is 2.95rad/s when the student starts at the rim.
The moment of inertia of the disk w.r.t rotational axis is
The moment of inertia of the student w.r.t. rotational axis when he is at the rim of the disk is
The total moment of inertia of the system when the student is at the rim is
The initial angular momentum is
And the initial kinetic energy of the system is
Now, when the student is at 0.883 m from the center, the moment of inertia of the student w.r.t. the axis of rotation is
So, the total moment of inertia of the system is
Now, the angular momentum of the system is
Conservation of angular momentum gives us
So, the final angular velocity is 9.65 rad/s.
Now, the final kinetic energy of the system is
It is notable that the kinetic energy of the system has been increased.
And the increase in the kinetic energy is
So, the total energy put in the system is 15844 J.
A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about...
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