Answer:
0.56191 rad/s
Step-by-step explanation:
r = Distance at which the ball is caught = 0.45 m
m = Mass of ball = 2 kg
v = Velocity of ball = 3 m/s
= Moment of inertia of stool student system = 4.4 kgm²
Initial angular momentum is

As the stool rotates the linear momentum is not conserved but the angular momentum is conserved.
Final angular momentum is

Moment of inertia is given by

= Moment of inertia of ball
As the angular momentum of the system is conserved

The angular speed of the stool is 0.56191 rad/s