Mass Moment of Inertia
Mass moment of inertia (sometimes called just "moment of inertia") is responsible for providing resistance against changing the rotational speed of a rotating body. The mass moment of inertia is represented by “I" in mechanical and structural design calculations.
The units of the mass moment of inertia are Kg-M², Gram-Cm², Lb-Inch² etc.
The general formula for calculating the mass moment of inertia can be given as:
I = ∫ r² dM………………….1.1
I – Mass moment of inertia.
dM – A very small mass parallel to the desired axis.
r – Distance of the small area from the axis.
However, you need not to use this equation most of the time as mass moment of inertia values for standard geometries are readily available.
The mass moment of inertia is the rotational analog of mass. That means, in all the rotational equations of angular momentum, angular kinetic energy, force etc. the mass moment of inertia (I) should be used.