![]() ![]() ![]() So, for instance, the center of mass of a uniform rod that extends along the x axis from \(x=0\) to \(x=L\) is at (L/2, 0). The center of mass of a uniform rod is at the center of the rod. A uniform thin rod is one for which the linear mass density \(\mu\), the mass-per-length of the rod, has one and the same value at all points on the rod. The simplest case involves a uniform thin rod. for all the point masses that make up the object. In the simplest case, the calculation of the position of the center of mass is trivial. By accurately calculating the moment of inertia, engineers and architects can design safer and more efficient structures. We defined the moment of inertia I of an object to be. The ideal thin rod, however, is a good approximation to the physical thin rod as long as the diameter of the rod is small compared to its length.) The stress in a bending beam can be expressed as. A physical thin rod must have some nonzero diameter. ![]() The easiest rigid body for which to calculate the center of mass is the thin rod because it extends in only one dimension. Quite often, when the finding of the position of the center of mass of a distribution of particles is called for, the distribution of particles is the set of particles making up a rigid body. The center of mass is found to be midway between the two particles, right where common sense tells us it has to be. ![]()
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