(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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![(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1adcbf8c-bd95-4e2a-b3db-fdf2751069bf%2Fa06a346a-7bae-4820-a5bf-e680e939174d%2Fsp3mlu_processed.jpeg&w=3840&q=75)
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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