![]() ![]() Knowing that the desired axis of rotation is transverse, therefore we need to apply perpendicular axis theorem which states: In the problem we are required to find moment of inertia about transverse (perpendicular) axis passing through its center. Observe from figure 2, that this moment of inertia has been calculated about #z# axis. We know that moment of inertia of a circular disk of mass #m# and of radius #R# about its central axis is is same as for a cylinder of mass #M# and radius #R# and is given by the equation ![]() Since #V=”Areal of circular face”xx”length”=pi R^2L#, we obtain If #dm# is the mass of one such disk, then Let us consider that the cylinder is made up of infinitesimally thin disks each of thickness #dz#. We know that its density #rho=”Mass”/”Volume”=M/V#. Let us consider a cylinder of length #L#, Mass #M#, and Radius #R# placed so that #z# axis is along its central axis as in the figure. Integrating over the length of the cylinder.īut first of all let’s state the problem. Application of Perpendicular Axis and Parallel axis Theorems.ģ. Stating of a infinitesimally thin Disk.Ģ. ![]()
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