Starting from the angular velocity, we can calculate the tangential velocity of the stone:
[tex]v=\omega r= (12 rad/s)(0.5 m)= 6 m/s[/tex]
Then we can calculate the angular momentum of the stone about the center of the circle, given by
[tex]L=mvr[/tex]
where
m is the stone mass
v its tangential velocity
r is the radius of the circle, that corresponds to the length of the string.
Substituting the data of the problem, we find
[tex]L=(2 kg)(6 m/s)(0.5 m)=6 kg m^2 s^{-1}[/tex]
