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As far as I understood, we define two quantities:

  1. Inertia Tensor - a $3\times3$ matrix, which describes the object "mass" of rotation in relation to a certain point, helping us calculating rotations around any axis in 3D-space.

  2. Moment of Inertia - a scalar which describes the object "mass" of rotation in relation to a certain axis.

And my question is:

  • Is my understanding correct?
  • How can we reach the Moment of Inertia of some arbitrary axis, while being given the Inertia Tensor?
Taru
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  • Suggestion: Besides inertia tensor and moment of inertia also ask about products of inertia. – Qmechanic Feb 14 '17 at 23:51
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    Related: http://physics.stackexchange.com/q/66350/2451 , http://physics.stackexchange.com/q/60843/2451 – Qmechanic Feb 15 '17 at 00:02
  • Thanks @Qmechanic, It helped me understanding the subject, but I still have not reached a final conclusion about my second question "How can we reach the Moment of Inertia of an arbitrary axis, while being given the Inertia Tensor?"... – Taru Feb 15 '17 at 07:31
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    In short: By projecting the inertia tensor to that axis. – Qmechanic Feb 15 '17 at 09:58
  • @Qmechanic As a moderator, should I delete this question? or would you like to post an answer to this question, so I can accept it? – Taru Feb 15 '17 at 11:23
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    In principle, there's no difference for using inertia tensor and moment of inertia when the axis aligns exactly on one of the principal axes. However, the stability will be completely different. See this for your further interest. – Ng Chung Tak Feb 15 '17 at 11:29

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