1. Consider a solid cone with uniform density p, height h, and circular base wit
ID: 2305320 • Letter: 1
Question
1. Consider a solid cone with uniform density p, height h, and circular base with radius R (hence mass M-3phR2). Let the vertex of the cone be the origin of the body frame. By symmetry, choose basis vectors e, for the body frame such that the inertia tensor lj is diagonal. Will this rigid body with this body origin be an asymmetric top, a symmetric top, or a spherical top? Calculate the inertia tensor in this basis. How will the inertia tensor change if we change the body origin to the center of mass while the basis vectors remain fixed? Hint: Steiner's parallel axis theorem might help with this part of the problem.Explanation / Answer
what we will find is that one can calculate a single inertia tensor through a point that takes account of the shape of the object independent of the axes of rotation, and once that is established the angular moment through that established point can be determined easily.
one of the main property of the inertia tensor is that the diagonal elements are symmetrical so the inertia will remain sane in either positions as the cone shape is symmetry.
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