The rotational inertia of the combination is 21.5kg m2
Given that mass of ring = 10kg , outer radius 1.5 m and inner radius 1.2 m
Radius of ring = ½(1.5+1.2) =1.35m
Mass of solid sphere=8kg
Radius of sphere =1.2m
A combination rotational inertia of ring and solid sphere is addiction of rotation inertia of ring and solid sphere
Rotational inertia of ring Ir=MR^2
Rotational inertia of solid sphere Is=2/5MR^2
Combination rotational inertia of ring and solid sphere
I=Ir+Is
=M1R^2+2/5M2R^2
=(10)(1.3^2)+⅖(8)(1.2^2)
=16.9+4.608
=21.5kg m2
Hence the rotational inertia of the combination is 21.5kg/m^2
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