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 (a) through its center?

Video transcript

Welcome back, everyone in this problem. We want to figure out what the moment of inertia is of a vinyl record with a diameter of 15 centimeters and a mass of 30 g when it rotates around an axis perpendicular to its center. A says it's 1.2 multiplied by 10 to the negative fifth kilogram square meters. B 3.4 multiplied by 10 to the negative fifth kilogram square meters. C 5.5 multiplied by 10 to the negative fifth kilogram square meters and D 8.4 multiplied by 10 to the negative fifth kilogram square meters. Now, what do we know about the moment of inertia that can help us? Well, recall that the moment of inertia for a thin circular object rotating around its center is given by the formula I equals a half of Mr R squared. So if we have the mass of our object and its radius, then we should be able to figure out its moment of inertia. Do we have that information in our problem? Well, yes, we do notice that we are told that the diameter of our vinyl record is 15 centimeters, which means that its radius is going to be a half of 15 centimeters or 7.5 centimeters, which is the same thing as 0.075 m. We're also told that the mass of our object is 30 g, which is the same thing as 0.03 kg. So now that we have the radios and we have the mass, then we will be able to find a moment of inertia because by substituting those values, we'll get it to be equal to a half of 0.03 kg multiplied by 0.075 m squared. When we go ahead and solve, we should get it to be equal to 8.4375 multiplied by 10 to the negative fifth kilogram square meters. And if we write that to two significant figures, it will be approximately 8.4 multiplied by 10 to the negative fifth kilogram square meters. Therefore D is the correct answer. Thanks for watching everyone. I hope this video helped.