Hey, guys. So in this quick video, I'm going to show you how the moment of inertia of a system has to do with how the mass is distributed, how the masses are spread out, around the axis of rotation. Let's check it out. It says here the moment of inertia, I, has to do with how mass is distributed, how it's spread out, around an axis of rotation. So here we have a solid disk that has small masses. This is the disk and the masses are the black dots, the 4 black dots. And they're arranged in 3, not 2, 3 different ways. And I want to know in which of these, will the moment of inertia be greater? In which of these will the moment of inertia be greater?

Now this is a composite system with a bunch of different masses. So the total moment of inertia of the system would be the moment of inertia of the solid disk, which is a solid cylinder, plus the moment of inertia of the 4 masses. Okay? So something like i1 + i2 + i3 + i4. Now these three situations have the same disk with the same mass with the same radius. So for all of them, this is going to be the same. The only thing that will change is this. So the difference will be in how the tiny masses are arranged around the disk.

Now, if these are point masses, which they should be treated as point masses because it says here small mass, the equation for them is mr2. So you have a bunch of mr2, right? Four times. Now if you have the same four masses everywhere, these m's will also be the same. So it's going to come down to the r's for each mass. In other words, how far from the axis of rotation they are. Okay. So basically, the farther the masses are, the greater their individual moments of inertia will be and the greater the total moment of inertia of the system will be. So this one has to be the one with the greatest I. Okay? So I'm going to call this a, b, and c. And b is the greater one.

Now and that's because the masses are farther out from the center. C is the smallest, the lowest value of I because the masses are congregated in the middle. Here, you can see 4 masses really close to the center. Here, you'll see 4 masses really far from the center. And this guy is somewhere in the middle. 2 are far and 2 are close. So I'm going to say that the moment of inertia of b is the greater and the moment of inertia of c is the smallest. Okay? So greatest, smallest, and a is in the middle. This means that you can think of b as being the heaviest of the 3. Okay? Even if the masses are the same, it's got the most inertia. Another way that this question could be asked is, you know, if you apply the same force to it, who's going to rotate faster? Right? Well, this guy is the heaviest, so it's also going to be the slowest. Okay? Alright. So that's it for this one. Let's keep going.