Question
Thu February 17, 2011 By: Priyadarshini Selvam

I always have problem in finding out the moment of inertia. please tell me step by step on how to find the moment of inertia.

Expert Reply
Thu February 17, 2011
Dear student,
 

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 (lbm ft2, kg m2)

m = mass (lbm, 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 mi ri2 = m1 r12 + m2 r22 + ..... + mnrn2        (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

Hope this helps
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