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The kinetic energy of a rigid body is T = włlw where w is the angular velocity vector and I is
the tensor of inertia matrix. Let the kinetic energy of the body is T = 3w; - 4w102 + 602. Find
the kinetic energy of rotating body along the principal axes.​

Answer 1

Answer:

Most of us are familiar with the formula  12Iω2  for the rotational kinetic energy of a rotating solid body. This formula is adequate for simple situations in which a body is rotating about a principal axis, but is not adequate for a body rotating about a non-principal axis.

I am going to think of a rotating solid body as a collection of point masses, fixed relative to each other, but all revolving with the same angular velocity about a common axis – and those who believe in atoms assure me that this is indeed the case. (If you believe that a solid is a continuum, you can still divide it in your imagination into lots of small mass elements.)