I'm curious as to the formula used in Solid Works to calculate the Moment of Inertia of a Diamond/Double Cone. I believe the formula incorrect. The current formula being used is Iz-axis = 3/10 MR*2(R squared). In actuallity, the correct formula should be Iz-axis=3/5 MR*2(R squared). http://www.lane1bowling.com/pdf/Theoretical_Calculations.pdf This has been bothering me for quite some time. Your thoughts..?

Hi Richie,

I think that the PDF that you reference is incorrect, or unclear at best. I believe the formula should be Iz-axis = 3/10 MR*2(R squared) for both cases of a cone and a double cone, as long as the mass being referenced is the mass of the cone in the first place and the double cone in the second. The reference PDF may be saying that the formula for a double cone is double that of the single cone because the mass doubles (so they are referencing the single cone mass in the second equation). But this is very misleading.

I can't find another reference for the moment of inertia of a double cone, but there are many references for the moment of inertia of a sphere and of a half sphere (hemisphere) and the moment of inertia formulas for the Z direction are exactly the same for both. Here are two references that show this:

http://www.civilengineeringdegrees.net/2012/04/center-of-gravity-mass-moment-of.html

http://engineering-references.sbainvent.com/dynamics/mass-moment-of-inertia.php#.U8z7i7HD8eN

If a sphere and a half sphere have the same formula in Z, then the cone and double cone cases should as well since they are very similar types of geometry. Make sense?

I hope this helps,

Jim