MASS VS. WEIGHT

Mass and weight are often used interchangeably but they are NOT interchangeable.

Mass is the quantity of matter
Weight is the force exerted on the mass by gravity

The relationship is W = Mg
    where
        M = Mass
        W = Weight
        g = gravity

More generally: F = Ma
    where F is the force required to accelerate a Mass M at a rate a.

Typical units:
  Mass: kg, slug, lb-sec²/in
  Weight: lb, Newtons, kg-m/sec²

Mass is always a constant positive quantity.
Weight is a positive quantity which varies with gravity.

Neither weight nor mass require a coordinate system for definition.

CENTER OF GRAVITY LOCATION

Center of gravity location can be defined as:
- The balance point of an object
- The point through which a force will cause pure translation
- The point about which gravity moments are balanced

The center of gravity (CG) is also called center of mass.

The center of gravity location must be referenced to a 3 dimensional coordinate system. CG location is directly a function of the coordinate system in which it is referenced. It is measured relative to a reference datum using moment balance equations.

MOMENT OF INERTIA (MOI)

Moment of inertia is the characteristic of an object to resist rotation. The relationship is T = Ia
  where
    T is the torque applied to the object
    I is the moment of inertia of the object
    a is the resulting rotational acceleration

MOI must be referenced to a rotational axis. It is dependent on MASS DISTRIBUTION.

The moment of inertia of an object is the summation of MOI of point masses making up the object. The MOI of each element is I = Mr²
  where
    M is the mass of the element
    r is the distance of the element from the axis of rotation

Moment of inertia units: lb-in² or lb-in/s²

PRODUCT OF INERTIA

Product of inertia is the characteristic of an object which causes dynamic unbalance.

The relationship is P = M * X * Y
  where
    P is the product of inertia in a given (X-Y) plane for any (point) element of mass in the object
    M is the mass of the element
    X and Y are the coordinates of the element.

The product of inertia (POI) of the object is the summation of POI of the point masses making up the object.

POI may be positive or negative. The algebraic signs of the element coordinates MUST BE used to get the correct sign of the POI sum.