let
T be the tensio on the rope.
from the newtons 2 nd law
we have T - mg = ma
T = m ( g+a)
since the box has an upward accleration a = 0.80m/s2
the tension is given by
T = ( 30kg ) ( 9.8m/s2 + 0.8m/s2 ) = 318N
the rotation of device is described by
from the diagram
Fapp R - Tr = τ = Iα = I a/r
then moment of inertia can be obtaind by
I = r ( Fapp R - Tr/a) = (0.20m ) ( 140 N) ( 0.50m) - (318N)(0.20m)/ 0.80m/s2
I = 1.6kg- m2