Polar moment of inertia is

The moment of inertia for an area relative to a linear or axis perpendicular to the plane of the area

The moment of inertia for an area relative to a line or axis parallel to the centroidal axis

Applicable to masses whereas moment of inertia is applicable to area only

Dimensional Formula of Moment of Inertia and its Derivation

The dimensional formula of moment of inertia is given by,

M¹L²T⁰

Where,

Moment of Inertia (MOI) = Mass × [Radius of Gyration]². . . . (1)

Since, the dimensional formula of mass = M¹L⁰T⁰. . . . . . (2)

And, the dimensions of the radius of gyration = M⁰L¹T⁰. . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Moment of Inertia = Mass × [Radius of Gyration]²

Or, MOI = [M¹L⁰T⁰] × [M⁰ L¹T⁰]² = M¹L²T⁰.

Therefore, the moment of inertia is dimensionally represented as M¹L²T⁰.

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