If the M.I of a disc about an axis tangential and parallel to its surface is I, then its M.I about the axis tangential but perpendicular to the surface is

Dear GAutham,

Moment of Inertia (Mass Moment of Inertia) - I -  is a measure of an object''s resistance to changes in rotation direction. Moment of Inertia has the same relationship to angular acceleration as mass has to linear acceleration.

For a point mass the Moment of Inertia is the mass times the square of perpendicular distance to the rotation reference axis and can be expressed as

I = m r²         (1)

where

I = moment of inertia (lb_m ft², kg m²)

m = mass (lb_m, kg)

r = distance between axis and rotation mass (ft, m)

That point mass relationship are basis for all other moments of inertia since any object can be built up from a collection of point masses.

I = ∑_i m_i r_i² = m₁ r₁² + m₂ r₂² + ..... + m_nr_n²        (2)

For rigid bodies with continuous distribution of adjacent particles, the formula is better expressed as an integral

I = ∫ r² dm         (2b)

where

dm = mass of an infinitesimally small part of the body

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