Answer:
0.56191 rad/s
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
[tex]I_1[/tex] = Moment of inertia of stool student system = 4.4 kgm²
Initial angular momentum is
[tex]L_i=mvr[/tex]
As the stool rotates the linear momentum is not conserved but the angular momentum is conserved.
Final angular momentum is
[tex]L_f=I\omega[/tex]
Moment of inertia is given by
[tex]I=I_1+mr^2[/tex]
[tex]mr^2[/tex] = Moment of inertia of ball
As the angular momentum of the system is conserved
[tex]L_i=L_f\\\Rightarrow mvr=(I_1+mr^2)\omega\\\Rightarrow \omega=\frac{mvr}{I_1+mr^2}\\\Rightarrow \omega=\frac{2\times 3\times 0.45}{4.4+2\times 0.45^2}\\\Rightarrow \omega=0.56191\ rad/s[/tex]
The angular speed of the stool is 0.56191 rad/s
