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## Main Question or Discussion Point

Hi there, I was hoping that someone here could maybe give me a hand with a couple of issues I'm having to do with moments of inertia.

For a right circular solid cone of mass m, height h and base radius a, we have to show that its moment of inertia about a line through its vertex and perpendicular to this axis of symmetry is 3/20ma^2 + 3/5mh^2

In the earlier part of the question I was able to work out the m.o.i about its axis, but I'm really stuck on this part. I'm also not sure about using the inertia tensor and I don't think that's expected of us. I was thinking that maybe I could calculate it's m.o.i about a line parallel to this one through its centre of mass and then use the parallel axis theorem, but I'm not too sure about this and I wouldn't be too confident about even working it out this way. From this answer we have to find the moment of inertia of the cone about a diameter of its base, and I think we can use the perpendicular axis theorem for this bit using the 2 previous parts obtained.

Anyway, enough of my blethering. Any help would be fantastic and would potentially save me from brain damage due to excessive amounts of banging my head off the desk. :yuck: Thanks!

For a right circular solid cone of mass m, height h and base radius a, we have to show that its moment of inertia about a line through its vertex and perpendicular to this axis of symmetry is 3/20ma^2 + 3/5mh^2

In the earlier part of the question I was able to work out the m.o.i about its axis, but I'm really stuck on this part. I'm also not sure about using the inertia tensor and I don't think that's expected of us. I was thinking that maybe I could calculate it's m.o.i about a line parallel to this one through its centre of mass and then use the parallel axis theorem, but I'm not too sure about this and I wouldn't be too confident about even working it out this way. From this answer we have to find the moment of inertia of the cone about a diameter of its base, and I think we can use the perpendicular axis theorem for this bit using the 2 previous parts obtained.

Anyway, enough of my blethering. Any help would be fantastic and would potentially save me from brain damage due to excessive amounts of banging my head off the desk. :yuck: Thanks!