Accelerations of boy on carousel

by Patrick Ford
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All right. So in the second example, we have carousel now 16 m and radius. So it's draw a circle here, and the radius is 16 and it accelerates from rest with this. So Omega initial zero in Alfa is 0.5 boy stands at the edge again. So the little are the distance between the center and the boy is just the same 60 m and we wanna know After seconds, Delta t equals 10 seconds. What is his tangential velocity Now I'm gonna put it over here to the side because tangential velocity v t is not one of his five motion equations. So I'm just organizing. It's a little bit. I wanna know his tangential velocity. Remember, tangential velocity or linear velocity of an object at a point in the disk is just given by our Omega, where r is the distance from the center and omega is the angular speed. Okay, I know are 16 but I don't have w So we're gonna have to do here is we're gonna have to find w final, which we're going to do using motion equations. Okay, variable that's missing here is Delta theta. So I'm gonna put a little sad face. And this tells me that the equation I should use is the first one. Because it's the only equation that doesn't have Delta theta or make a final equals and making initial plus Alfa, um, t and we're looking for Make a final. This is zero Alfa is 0.5 The time is 10. So Omega's just point five radiance per second. I can plug this in here. This is 16 times 160.5, which means the velocity will be 8 m per second for part B. I want a little tangential acceleration. Um, a T is our Alfa and I have both numbers, so we can split in 16 alphas 160.5 eso This is going to be zero point a I'm sorry pointing, um, 0.8. Same thing meters per second squared. Okay. Yep, that's it. And then see, I'm looking for the radio acceleration A rad, which is the same thing as a centripetal a C. And I can use V square over our or I can use our omega squared. It's gonna use this one already have V, so it's gonna be eight squared. Are is 16. So the answer will be eight square by by 16 is four. So 4 m per second squared for part D. I want to know the angular acceleration, angular accelerations, Alfa Um, angular acceleration is Alfa. We actually already have the angular acceleration, so it's just going to be 0.5 Okay, this one is the freebie. Just make sure you know what you're doing. Um, radiance per second square. And the last one is a total linear acceleration, which is a and A is the square root of the other two linear acceleration. That's another way to think about this. There's three linear. One of them combines the other two, so it's a T square plus a c squared. And if you plug this in its points eight squared four squared. You combine all of this and you get 4.1 m per second squared, and these are the final answers. All right, that's it for this stuff. Um, let me know if you have any questions.