To solve this problem it is necessary to apply the concept related to the Angular Moment.
By definition the angular momentum is given as
[tex]L=mvr[/tex]
Where
L= Angular momentum
m= mass
v= linear velocity
Recall that line speed can also be expressed as a function of angular velocity as
[tex]v = \omega R \rightarrow[/tex]where [tex]\omega[/tex] is the angular velocity and R the Radius
For the case described in the statement we have that there are two distances in different components, therefore the net radius would be given by
[tex]r^2 = R^2+d^2[/tex]
Where
R= Radius of the block
d= displacement in z-axis
Replacing with our values we have,
[tex]r^2=0.4^2+0.6^2[/tex]
[tex]r=0.7211m[/tex]
Replacing in the angular momentum equation, depending on the angular velocity we have to
[tex]L=m(\omega R)r[/tex]
[tex]L=(2)(16*0.4)(0.7211)[/tex]
[tex]L = 9.23008Kg.m/s[/tex]
Therefore the magnitude of the component in the xy plane of the angular momentum around the origin is [tex]9.23008Kg.m/s[/tex]
