Part of the Dynamics course offered by the Division of Applied Mechanics, School of Engineering and the Engineering and Technology Portal
Contents 
The center of gravity (or mass), abbreviated as
COM, of any object is that point within the object
upon which gravity (or any body force) acts, regardless of the
orientation of the object. The COM of an object
may be calculated by using the principle of equilibrium. (See also
the List of centroids on
Wikipedia.)
, , (1)
In the event that the density ρ of an object is not uniform
throughout, the calculation of COM may be done by
a similar set of equations involving the addition of density to the
analysis.
, , (2)
If a body is made up of multiple sections, each of which has a unique mass, the method for evaluating the centroid of that body is to evaluate the composite body by finite element analysis of each of the sections through the use of moment balancing, as above.
, , (3)
Inertia is the resistance of an object in
response to attempts to accelerate it in a linear direction.
Inertia is considered the Inertial Force or Inertia Vector. The mass is a scalar, and the acceleration is a vector.
Mass Moment of Inertia is the
resistance of an object to attempts to accelerate its rotation
about an axis.
, , (4)
If the axis of rotation passes through the center of gravity of the rotating object, the calculated is called the Centroidal Mass Moment of Inertia. (See also the List of moments of inertia on Wikipedia.)
If the Centroidal Mass Moment of Inertia of a body is known, the
Parallel Axis Theorem may be used to determine the Mass Moment of
Inertia of that body around any axis parallel to the first axis of
rotation which passes through the center of gravity.
The radius of gyration ,
of a body is the distance from that body's rotational axis that the
COG may be before the mass moment of inertia changes.
and
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