Animation by Ames Bielenberg
This page describes the development of mathematical models of rotating mechanical systems, though some translate (move back and forth) as well. It is suggested that you read about translating mechanical systems first. Since many of the concepts involved with rotating systems are analogous to those in translating systems, many of the discussions in these pages will be brief.
A list of the fundamental units of interest is listed below. The next tab (above: "System Elements") gives a description of the building blocks of these system (inertia, spring and friction elements). This is followed by a description of methods to go from a drawing of a system to a mathematical model of a system in the form of differential equations ("Mathematical Model"). Methods for solving the equation are given elsewhere. The last section discusses topics relevant to energy storage and dissipation in these systems ("Energy Power").
This page does not discuss the solution of these equations, only the development of the equations through a physical model of the system.
The table below lists commonly used units of measure for Rotating
mechanical systems in SI units. More complete
tables are available.
|Fundamental Quantities||SI unit|
|Time - t||second (s)|
|Moment of Inertia - J||kilogram (kg-m²)|
|Angle - θ||radians (rad)|
|Torque - τ||Newton (N-m)|
|Energy - w||Joule (J) [W-s, N-m]|
|Power - p||Watt (W) [J/s]|
|Spring Constant - Kr||(N-m/rad)|
|Friction Coefficient - Br||(N-m-s/rad)|