CBSE Class 11-science Answered

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