Alright. So here we have an example, we're calculating the rotational velocity of the earth, as in two different situations as it rotates around itself and rotates around the sun. So let's look at the first one: earth around itself. Okay, so actually I want 𝒚 (omega) of earth around itself. Okay? Well, 𝒚 is either Δθ over Δt or 2πt or 2πf. Now, as the earth rotates around itself, what's the Δθ? What's the time? I'm not telling you how many degrees it's going through. I'm not telling you this either. So, one of the things you can do is you can then use some information you know about the earth. And you know how long the period of the earth is, how long the earth takes to make a complete revolution around itself. If it's a complete revolution around itself, that takes 24 hours. Right? So it takes 24 hours. So all I can do is I can just write 𝒚 equals 2π24 hours. Obviously, I can't just leave it as 24 hours. I have to convert. I have to convert that into seconds. Okay? So it's going to be 2π 24 times 60 times 60, and you multiply all of this, you get that 𝒚 for the earth is 7.27 ×10 to the negative 5th radians per second. It's a very small number. That's because the earth takes a very long time to spin around itself, right, relative to, like, a DVD or something. Alright.
B, how long, or rather, what is the rotation velocity of the earth rotating around the sun? Very similar problem, 𝒚 equals, I can use any of these equations. In this case, what I'm going to use is again 2πt, and the period of the earth going around the sun is 365 days. K. And you don't have to worry about BPRs or any of that stuff. Just simplify it by doing this. So it's 2π 365. So it's basically all of this. This is one day, right, 24 hours. So it's all of this times 24, times 365. So I'm going to repeat the bottom there. And this is going to be an even smaller number. I get 1.99 ×10 to the negative 7 radians per second. Okay?
And then the last thing I want to point out to you guys is that if the earth is rotating around itself, in this case, we're talking about a we're talking about a rigid body that's spinning around itself because it's sort of a sphere, not exactly, but you can approximate it as a sphere that spins around itself, right? The earth rotating around the sun actually acts as a tiny point object. Why? Because relative to the size of the sun and relative to the distance between the 2, the earth is so tiny that you would consider it a point mass going around a circle. Here, you have a rigid body spinning around itself. So that's an important distinction in these two examples. An object can, depending on the situation, be thought of as a rigid body that spins around itself or a tiny point mass, that spins around, a circular path. Okay? That's it for this one. Hopefully, it makes sense. Let me know if you guys have any questions.
