5Rigid Body Rotational Dynamics
5.1 Moment of Inertia
The equations of motion of a rigid body that is constrained to rotate about a fixed axis are reviewed here briefly. Consider the cylinder shown in Figure 5.1.
Figure 5.1 Cylinder constrained to rotate about a fixed axis.
The approach here is to obtain the equations of motion of the cylinder by first obtaining an expression for its kinetic energy. To do so, denote the angular speed of the cylinder by 
and the mass density of the material making up the cylinder by 
. Then consider the cylinder to be made up of a large number 
of small pieces of material 
where the 
th piece has mass
This is illustrated in Figure 5.2. Each piece of mass is rotating at the same angular speed so that the linear speed of is where is the distance of ...
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