[Picture on LEFT is second part of question SORRY!] A)The diagram (on the right)

Question

[Picture on LEFT is second part of question SORRY!]

A)The diagram (on the right) shows a uniform thick sperical shell that will rotate about its diameter. The shell has a mass of M, and inner and outer radii equal to half the outer radius. Find the moment of inertia for the shell.  Express your answer in terms of the mass of the shell, M and the outer radius, R.

 When using I=2/5Mr^2 All I got was the very first step :   

I=2/5Mr^2 - 2/5M(1/2r)^2 

B) Now the shell is made to rotate about an axis thru its outer skin. Find the new moment of inertia for this rotation. Again express your answers in terms of the mass of the shell, M, and the outer radius, R.

The only clue I have is to use the parallel axis thereom (which just confuses me) it looks like:

I p.a.= I c.m. + M(d)^2 where d is the distance from the center mass to the actual rotation.

THANK YOU FOR ANY HELP I WILL RATE IF IT MAKES A LITTLE SENSE!

Explanation / Answer

shockingly you almost carried to completion. we find I of the disk which will be I c.m.=0.3MR^2 and then we use the second equation you gave and see that d is the distance from the center of mass to the point of rotation......which is R so we get I tot= I c.m.+M(R)^2 which can be simplified down to I tot= 1.3MR^2

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