Reprints Online

Determination of Moment of Inertia & Radius of Gyration of Flywheel (Part – V) 

Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, (SI units kg m², English units lbs ft2) quantifies the rotational inertia of a rigid body, i.e. its inertia with respect to rotational motion, in a manner somewhat analogous to how mass quantifies the inertia of a body with respect to translational motion. The symbols I and sometimes J are usually used to refer to the moment of inertia.

The (scalar) moment of inertia of a point mass rotating about a known axis is defined by

where

m is its mass,

and r is its perpendicular distance from the axis of rotation.

The moment of inertia is additive so, for a rigid body consisting of N point masses mi with distances ri to the rotation axis, the total moment of inertia equals the sum of the point-mass moments of inertia

Generalizing to a solid body described by a continuous mass-density function , the moment of inertia for rotating about a known axis can be calculated by integrating the moments of the point masses relative to the rotation axis

where

V is the volume region of the object,

r is the distance from the axis of rotation,

m is mass,

v is volume,

ρ is the pointwise density function of the object,

and x, y, z are the Cartesian coordinates.

The moment of inertia for non-point objects can also be found or approximated as the product of three terms:

where

k is the inertial constant,

M is the mass, and

R is the radius of the object from the center of mass.

Inertial constants are used to account for the differences in the placement of the mass from the center of rotation. Placing all the mass on the outside of the disk would provide for the biggest inertial constant. For example:

·      , thin ring or thin-walled cylinder around its center,

·      , solid sphere around its center.

Compiled by Samar Das