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Moment of India is a tensor quantity but consider as scalar why?
Asked by krishnasingh56541220 | 30 Jul, 2023, 01:33: PM
Moment of Inertia of system of particles about an axis depends on the orientation of axes relative to system of particles.

Moment of inertia is expressed as

. . . . . . . . . . . . . . (1)
Moment of inertia I expressed above is Moment of inertia tensor .

Where individual elements are expressed as

;         ;      ;

;      ;   ;

Given a unit vector in the direction of rotation axis , then moment of inertia about its axis is given by
=
Moment of inertia tensor is symmetric matrix and therfore it can be diagonalised by orthagonal transformation of cartesian axes.
It is essentially a reorientation of the orthagonal axes system. If the coordinate system is reoriented in this way ,
then moment of inertia tensor becomes diagonal, i.e., it has the form

.................... (2)
The three diagonal elements are called principal components of moment of inertia and the corresponding axes that lead
to this diagonal form are the principle axes of the system of particles for which we want to get moment of inertia.

Each individual elements , i.e., Ixx , Iyy and Izz are just numbers. hence they are scalar .

Where as the whole matrix I is tensor .

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