Calculate the moment of inertia of each of the following uniform objects about the axes indicated. Consult Table 9.2 as needed. (a) A thin 2.50-kg rod of length 75.0 cm, about an axis perpendicular to it and passing through (i) one end and (ii) its center, and (iii) about an axis parallel to the rod and passing through it.

Video transcript

Hello everyone. So in this problem we're given a thin spoke of mass three kg. That is 100 cm long. To be used in an experiment and we want to determine this moment of inertia around three perpendicular axes, One of its ends through the center and also a parallel access through the spoke. So for the first scenario we have some smoke. We want to rotate it about one of its ends and we recall that the moment of inertia equation, we spoke about one of its ends. It's just one third ml squared. We have the mass of the spoke and the length. So we can make this substitution. At the moment of inertia It's equal to 1/3 time three kg times 100 cm, which is just one m squared. And we get that I is equal to one kg times meters spread. For the second scenario, we have some scope and we want to rotate it about the center perpendicular all but the moment of inertia equation for this scenario is 1 mm elsewhere we can make the same substitution. So the moment of inertia is 1 12 times three kg Times one m square. And you get that it is 0.25 kg times m square. Third scenario, we have a smoke, we want to rotate it around its central axis. But the assumption we make when solving these problems is that the mass is centered around the central axis. So considering this assumption R is equal to zero for all the point masses. Since I is equal to the sum of my times are I square and a car is equal to zero. Then the moment of Inertia for this scenario would just be equal to zero kg and m squared. So for the first one is one, the second one is 10.25, and the third one it is zero. So the answer to this problem would be be so have a great day.