The motion of any particle is most easily described by using the the equations of Rectilinear Motion. Where represents distance or displacement, represents velocity and represents acceleration, it may be remembered from Physics that:
The motion of any particle along a curved path is most easily described by using the the equations of Curvilinear Motion. Where represents the position of a particle in cartesian or polar coordinates and is the displacement of said particle, the scalar quantity represents the distance of the displacement and is the instantaneous velocity of the particle:
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)
For a system of two vectors oriented in different directions, the relationsip between the two may be establshed through vector addition. For vectors and , the relative motion of from the frame of reference of is:
The calculation of relative motion is completed similarly for acceleration.