Answer:
2.8 rad/s
Explanation:
In absence of external forces, the total angular momentum of the system must be conserved.
The angular momentum when the arms of the student are extended horizontally is given by:
where:
is the moment of inertia of the student+stool
is the moment of inertia of each mass, where:
m = 2.6 kg is one mass
r = 0.71 m is the distance of each mass from the rotation axis
is the initial angular velocity
So we have
When the student pulls the weights to a distance of r' = 0.23 m, the angular momentum is:
where:
is the new moment of inertia of each mass, with
r' = 0.23 m
Since the angular momentum must be constant, we have:
and solving for , we find the final angular velocity: