(i) Show that all three principal moments of inertia of a solid regular dodecahedron are equal. Hint: you do not need to compute their values. (ii) A rigid body consists of 12 identical thin rods of length a, forming the edges of a cube. Each of the rods has mass m and a uniform mass density. Calculate the moment of inertia tensor of the body.
(i) Show that all three principal moments of inertia of a solid regular dodecahedron are equal. Hint: you do not need to compute their values. (ii) A rigid body consists of 12 identical thin rods of length a, forming the edges of a cube. Each of the rods has mass m and a uniform mass density. Calculate the moment of inertia tensor of the body.
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Transcribed Image Text:(i) Show that all three principal moments of inertia of a solid regular dodecahedron are equal.
Hint: you do not need to compute their values.
(ii) A rigid body consists of 12 identical thin rods of length a, forming the edges of a cube. Each of the
rods has mass m and a uniform mass density. Calculate the moment of inertia tensor of the body.
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