A 12-cm-diameter DVD has a mass of 21 g. What is the DVD's moment of inertia for rotation about a perpendicular axis (b) through the edge of the disk?

Video transcript

Welcome back, everyone. We are making observations about a bicycle wheel. You're told that it has a radius of 15 centimeters or 0.15 m and that it has a mass of 1.5 kg. Now, we are tasked with finding what is going to be the moment of inertia about the rim of the wheel. Now, before getting started here, I do wish to acknowledge our multiple choice answers on the left hand side of our screen here. Those are going to be the values that we strive for. So without further ado let us begin. All right. Well, in order to calculate the moment of inertia at a point on the rim of the wheel, we are going to have the moment of inertia at the center of the wheel plus mass times our radius squared. But what is our inertia at the center of our wheel? Well, for a circle, really a disk here, what we have is that our moment of inertia is one half times the mass times radius squared. So let's go ahead and calculate that we have one half times 1. times 0.15 squared. What this gives us is that our moment of inertia about the center of the wheel is 0. kg meters squared. Great changing colors. Here we are now ready to find the moment of inertia at a point on the rim of the wheel. So what does this give us? Well, according to our formula, we have 0. plus 1.5 times 0. squared. And what this gives us is 50.6 times 10 to the negative third kilograms meters squared corresponding to our final answer choice of a Thank you all so much for watching. I hope this video helped. We will see you all in the next one.