Hi, everybody. So, for this one, we didn't know what. The projector has a weight of £45. And with respect, symmetry determines proximity. Rate of session Be, um, if it's further know the radius of the gyration of the special and determined exact values of the two possible razor procession. Okay. And we can start by kind of drawing a little image. Um, my image, of course, is not gonna be a perfect not stupid. Good. Sorry. Had something on the screen here. So there we go. Andi, it looks like a little bullet. So and here we have. Sure that's what they show in the image. So I'm just coughing the image that they have. Um, but you can do your own image if it helps, but I like to kind of copies of these images that it helps me think it through. It's also just nice that someone helps you know you with your thinking. Okay. And so it is moving this way. Okay, because you know how Ebola is actually spinning, okay. And from about here to hear way have d and then here is beta angle beta. And from about here, Thio here we have C okay on eso now express the drag force due to the first couple system. And so the drag force is gonna equal thio um, de hoops That does not look like a d does it? Eagle thio d sign Beta minus w co sign Beta and I had okay. And, um okay, so can the drag force is an atmospheric drag force. Okay? And we need express the moment about G. So the moment here about G on that's gonna be expressed with m g equals D. Okay, let me make my I am sorry. I cannot write these today. Apparently. So D si side beta j hat. Okay. And now here the g is mg and distance between G is CP. Okay. And so we have the data equals beta equals three degrees. Okay. And express the moment about the mass center and express the moment and essentially has little hatchet m g equals thio. I inertia w Z minus anoosha. Bye. Co sign a data 552 different ways. Um, there are two different ways to write. Five. So you need to write by, like this or, um like this. I wish whether you can which other way I like to call this the Disney Fi. It looks like the Disney sig. Simple. Okay, sign data. And again, learning to write Greek letter is just right, um, but clear, precise everyone else, but kind of figure out which way you like for yourself. And so now we have to compare these two. So what we're gonna do is replace this here. Okay, so from that, we have d c sign beta J hat. And actually, we don't need the j hot here. Okay? And equals I the minus I by cosine data and yeah, I'm just saying the letters, um, because it's faster. Thio say the equation when I just do that. And so we're gonna call this equation three s. So we got to express the angular velocity here, and that's gonna be a capital five class little FYI, co sign data. Yeah, We're just gonna plug that in here. We're gonna scroll down. So we have d c sign they signed beta. Okay. Equals nurse Sha Times five plus little by co sign data. Okay. Minus I buy co sign data by sign data. And let's simplify this. So we have d c equals I Bye. Five. Um, plus A for the inertia five squared co sign data minus I five. Fire co sign data. And I believe, have I been riding down the thing? The longtime school time? Give me one second. Oops. And what we could do is actually replace this one up here with data. Because we did that here. Um, So since we've been placing that, here we go, Here we go. And this actually came to all of that, and that's what I was trying to figure out. Fix that and do this. And here we have d c equals I Bye bye. Minus I Inertia minus inertia. Five squared, co sign data. Okay. And so for this got neglect. We can neglect this term. And eh? So what we'll do is we have I Bye. Five is about equivalent to D. C. And so you're five is going to be about D. C. Over. Hi. Over Capital Five and way also have m equals weight over gravity. The mass. So we have £45 times 32.2 ft for a second squared equals 1.3975 I be squared and feet and this actually is equal to a slug. Here we go on where it's going to school down again on we can express the access Then. So we have the access thin from inertia here of em que busy square. And this is gonna be 1.3975 times two inches, which is times beat, divided by 12 inches squared. And in here we get 0.0 3882 slug be square. And now we can express your cap of five, which is the rate of spin as to pie in 60. So this is your weight of spin. Okay? Yeah. Here we go. And this one is two pi 6000 r e f okay, divided by 60. And we have 37 699 0.11 18 divided by 60. And we get 6. 28 0.32 radiance per second. Okay. And now weaken Dio is a and four A. What can do is we go back up to 25 on. We're using this equation here. So we're bringing that down here. Uh huh. And here we could substitute what? We have £25. Six inches times 1 ft, divided by 12 inches, Divided by 0.3882 Slug beef squared time 6 to 8 0.3 Thio lady in a second. Okay? And this is gonna equal thio 0.512 for radiance per second and we need to convert RPM. So it's 62 pi on is gonna equal to 4.89 r p m master rate of procession. So put rates No. Three session. Okay. And now for B. Yeah, we have to find the moment moment of inertia about K X, which is looks like this. And in here get 1.39 75 find a divided by 12 square equals 0.6211 slug feet squared. And, um, Now what we're gonna dio is plug it into, like, this whole thing into our equation that we had up above. So we're gonna plug it into this one right here. Yeah. Okay. I'll give you a second coffee guy down. Okay, so now I'm just gonna write it out. So we have 25 six inches divided by well eat walls and now right, 0.3882 Bye. 6 to 8.32 Radiance for second. It's not gonna put units here, so it saves us time. Why is the same units that I use up above here eso You should already know it. You can write them down. Helps you out. Okay, I'm just saving space. 0.6211 minus what's Oh e. I mean, it's that go minus 0.0 3882 times by squared times co signed to three Degrees Way. Don't need to make that that day. Here we go. Okay. So you can honestly town I would try to solve for this little bad. The five on was some simplified 12.5 equals 24.391 five minus 0.581 by square. And if we have it right, we have 0.581 I squared minus 24.3915 Mine bus 4.5 equals zero, And we could actually dio Oh, the classic formula here. Um, forget a formula just to help us. This is one of those formulas that you think you would never used to use. all the time. Physics. So remember it the nice Um, it's a really nice formula that a lot of Matthews is some reason even high up math. So it's a good one toe, remember? So we have 24.391 plus minus. Um, 24.391 squared minus four times 0.581 times 12.5 divided by two times 0.581 Yes. All right, five. Okay. And here we get 24.391 plus or minus. Um, 23.775 divided by 1.163 And from this you have 0.5189 radiance per second or 41.42 radiance per seconds. You're not quite done. So now we gotta convert these tow our PM. So we've been converted to R p M. And what we're gonna do is multiply both of these, Uh, bye. 60 two pi r p m radiance for a second, but you just multiply them each by bath. And so the first one you get 4.96 our PM and the second one we get 396 are Yeah. Okay. And those were your answers. Thank you, guys.