A thin uniform rod of mass M and length L is bent at its center so that the two segments are now perpendicular to each other. Find its moment of inertia about an axis perpendicular to its plane and passing through (a) the point where the two segments meet

Video transcript

Everyone in this problem, you make a corner weld between two thin uniform rods of mass, one kg and like 3m each. In this situation, the two rods are perpendicular to each other and were asked to determine the moment of inertia about an axis perpendicular to the plane of the system passing through the welding point. And so we can draw this. We have our two rods, they're welded together perpendicular early. Each one is three m long, And we also know that each one kg and we want to figure out the moment of inertia about the axis right here at the world point. So recall the moment of inertia for a rod about the end is going to be the mass M times the length squared, divided by three. Now in this case are two rods are identical. And so our total moment of inertia is just going to be two times the moment of inertia of a single rod, Which is going to be two Times M. elsewhere over three And substituting in our values and we have 2/3 The mass M, which is one kg times the length squared, three m all squared. This is gonna be 2/3 times one kg Times 9m Squared. And this gives us a moment of inertia of six kilogram meters squared. And so if we look at our answer choices, we see that the moment of inertia that we found for these uniform rods is c six kg meters squared. That's it for this one. Thanks everyone for watching. See you in the next video