Mass moments of inertia for axisymmetric shells evaluated using the Monte-Carlo method – Truncated conical shells

The mass moment of inertia (MMoI) of a truncated conical shell is derived. The MMoI of a truncated conical shell, can be used to model the MMoI for other shapes; a conical shell, a tube, a disc and an annulus. Using the additive property of MMoI, the MMoI for a spherical shell, and a hemispherical shell can also be calculated. The MMoI is evaluated using the Monte-Carlo method. Two variants of the Monte-Carlo method are derived, named No PAT method and PAT method, differentiated by whether the parallel axis theorem is combined with the Monte-Carlo method or not. The PAT method tends to be the more efficient algorithm. This paper provides a partial framework for evaluating the MMoI for any axisymmetric body. It is proposed that the calculation of MMoI, for a truncated conical shell, and truncated cones can be used to develop student project activities. By way of examples of potential student projects, the calculation of the MMoI using the Monte-Carlo methods, for the Saturn V rocket, and an American football are demonstrated.