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.

Asked by priyadarshini_selvam | 17th Feb, 2011, 01:45: PM

Expert Answer:

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
Team
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Answered by  | 17th Feb, 2011, 01:58: PM

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