Moment of Intertia of a cylinder rolling inside a cylinder

[Elanorin]

Hi all, I just have a troublesome time wrapping my head around the concept of moment of inertia of a cylinder inside a cylinder. For example, in the attached figure

The moment of inertia of the cylinder with radius 'r' around the point o, according to my understanding should be

$I_o = I_s+ m (R-r)^2$
Where

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$I_o$ is the moment of inertia around point o

​

$I_s$ is the moment of inertia of the small cylinder = $0.5 m r^2$

​

m is the mass of the small cylinder
I believe my understanding above is wrong, since the actual answer is $1.5 m (R-r)^2$. Any help to clarify is appreciated.

 

[paisiello2]

I think that there is an additional component caused by the fact that the smaller cylinder would also be rotating about it's own axis at the same time it is rotating about the larger cylinder's axis as well.