A flywheel is a rotating disc used to store energy. What is the maximum energy you can store on a flywheel built as a solid disc with mass 8 × 10 4 kg and diameter 5.0 m, if it can spin at a max of 120 RPM?

Hey guys, let's check out this practice problem. So here we have a flywheel that's used to store energy. So a flywheel is just a disc, usually a solid disc. And remember when you spin things, they gain, rotational kinetic energy. So you can think of the wheel as a source to store that energy because you can use the energy of the rotation for something else later. Cool? So it says here that it's a rotating disc. Now it doesn't explicitly say, but you can assume it is a solid disc. Whenever you hear disk, you think solid disk, unless obviously, it tells you that it's a different kind, at which point it'll probably be called a hoop or something like that. That's used to store energy. Now solid discs have moment of inertia of half mr square. It's the same moment of inertia of a solid cylinder. That's the most popular moment of inertia for physics problems. It's used to store energy. This energy is in the form of rotational kinetic energy. When you think of stored energy, you might think of potential energy. But in this case, it's rotational kinetic energy. I wanna know what is the maximum energy that you can store. So what is, we're going to call this e max. But in this case, I know that the energy is k r, so I'm going to write k r max. That's what we want to know. What's the maximum energy you can store on a flywheel that is built as a solid disk? Told you here explicitly that it's a solid disk with this mass and this diameter spinning at this RPM. So let's plug in these numbers. So mass is 8 times 10 to the 4th. Diameter is 5 meters. We don't use diameter. I'm going to change that into a radius of 2.5. And it's spinning at an RPM of 120 RPM. Okay. Now I want the maximum energy, and it can spin at a maximum RPM of 120. Remember, rotation is rotational energy is half I omega squared. If I want the maximum r, the maximum k r, then I want the maximum speed. The faster you move, the more energy you have. So if I want the maximum energy, I will be using the maximum r RPM here. Okay? So this is what I'm looking for. I just have to plug in numbers here. So let's expand this real quick. I is going to be half mr squared. And I want to point out that I have m and I have r. And then the next thing is omega. You don't have omega, but you can get omega from RPM. Right? Remember, RPM w is 2 pi f and f is remember f is RPM over 60. So I can rewrite this as RPM over 60. Okay? And we can quickly calculate this. 2 pi RPM is 120 divided by 60. So Omega is 4 pi radians per second. So what I can do is I can plug in 4 pi right here, and then I gotta square the whole thing. Okay. So you have 1 over 4, because the 2 halves combined, times the mass, which is 8 times 10 to the 4th, times the radius square, which is 2.5 square times 4 pi squared. We're done. It's just a matter of multiplying this whole thing. And if you multiply that you that you can store on this little wheel. Alright? So that's it for this one. Hopefully, you got it. Let me know if you have any questions.

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A flywheel is a rotating disc used to store energy. What is the maximum energy you can store on a flywheel built as a solid disc with mass 8 × 104 kg and diameter 5.0 m, if it can spin at a max of 120 RPM?

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A flywheel is a rotating disc used to store energy. What is the maximum energy you can store on a flywheel built as a solid disc with mass 8 × 10⁴ kg and diameter 5.0 m, if it can spin at a max of 120 RPM?