By calculating the moment of inertia of each cylinder, one then uses the Parallel Axis Theorem to calculate the moment of inertia of the composite body composed of three cylinders. The attachment also contains a formula to calculate the moment of inertia of a single cylinder given the radius and length, so no integrals are required at all for calculating the result.
I didn't quite understand that, sorry. I thought the parallel axis theorem only was for changing the axis of objects? All my three objects are attached at the same axis, so I didn't quite get how I use the theorem. Also, the link you sent didn't contain anything about combined objects?
Thanks for your answer, anyways, I'm just a grasping this consept completely.
Hi, sorry for the ambiguous description, the cylinders are glued together like in your b.) illustration, in other words the flat sides are glued together.
The three cylinders are actually just pipes short pipes about 20 and 8 cm in diameter and 2 mm thick, so the density of each cylinder is not constant since the mass is distributed near the rolling surface of the cylinders. So yes, in a way, the mass density is a function of the cylinder's radius, where the density is mostly 0, while it's constant at a distance equal to the radius of the cylinder, since it's like a hoop.
On the last page of my attachment, you will find a formula for calculating the moment of inertia of a hollow cylinder about its centroid. Since the cylinders are of different sizes, you can use the parallel axis theorem to calculate the moment of inertia of the composite body after you determine the location of the centroid of the composite configuration.