as the equivalent flywheel, whose radius is the radius of gyration. The integral of the squares of the radii all the portions of the ring with respect to their mass , also expressible if the ring is modelled as a collection of discrete particles as the sum of the products of those mass and the squares of their radii is the ring's moment of inertia, denoted . The rotational kinetic energy of the whole system of moving parts is , where is the angular velocity of the moving parts about the same axis as the moment of inertia. The kinetic energy of translation of the moving parts is , where is the total mass and is the magnitude of the velocity. This gives the formula for the total kinetic energy of the moving parts of a machine as . Representing moving parts in engineering diagrams In technical drawing, moving parts are, conventionally, designated by drawing the solid outline of the part in its main or initial position, with an added outline of the part in a secondary, moved, position drawn with a phantom line (a line comprising "dot-dot-dash" sequences of two short and one long line segments) outline. These conventions are enshrined in several standards from the American National Standards Institute and the American Society of Mechanical Engineers, including ASME Y14.2M published in 1979. In recent decades, the use of animation has become more practical and widespread in technical and engineering diagrams for the illustration of the motions of moving parts. Animation represents moving parts more clearly and enables them and their motions to be more readily visualized. Furthermore, computer aided design tools allow the motions of moving parts to be simulated, allowing machine designers to determine, for example, whether the moving parts in a given design would obstruct one another's motion or collide by simple visual inspection of the (animated) computer model rather than by the designer performing a numerical analysis directly. See also Kinetic art — sculpture that contains moving parts Movement (clockwork) — the specific name for the moving parts of a clock or watch References Further reading Machinery