Rotational Inertia Of A Wheel

Moment of Inertia, General Form

Since the moment of inertia of an ordinary object involves a continuous distribution of mass at a continually varying distance from any rotation axis, the adding of moments of inertia generally involves calculus, the discipline of mathematics which tin handle such continuous variables. Since the moment of inertia of a signal mass is defined by

and so the moment of inertia contribution by an infinitesmal mass element dm has the same form. This kind of mass element is called a differential element of mass and its moment of inertia is given by

Note that the differential element of moment of inertia dI must e'er exist divers with respect to a specific rotation axis. The sum over all these mass elements is chosen an integral over the mass.

Usually, the mass element dm will be expressed in terms of the geometry of the object, so that the integration can be carried out over the object every bit a whole (for example, over a long uniform rod).

Having called this a full general course, it is probably appropriate to betoken out that it is a general form simply for axes which may exist called "master axes", a term which includes all axes of symmetry of objects. The concept of moment of inertia for general objects about arbitrary axes is a much more complicated subject. The moment of inertia in such cases takes the form of a mathematical tensor quantity which requires nine components to completely ascertain it.

Rotational Inertia Of A Wheel,

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

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