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A small clamp of mass $m_{B}$ is attached at $B$ …

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Problem 114 Easy Difficulty

A small clamp of mass $m_{B}$ is attached at $B$ to a hoop of mass $m_{h^{\prime}}$ The system is released from rest when $\theta=90^{\circ}$ and rolls without sliding. Knowing that $m_{h}=3 m_{B},$ determine $(a)$ the angular acceleration of the hoop, $(b)$ the horizontal and vertical components of the acceleration of $B$

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Physics 101 Mechanics

Vector Mechanics for Engineers: Statics and Dynamics

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Video Transcript

Hello. So, for this question, we want to find the angle A celebration of the set up. Um, so just a quick reminder. So when I set up like this, So at this point, you're gonna have to components of the acceleration. I thought I'm like that, uh, and it's going to be another acceleration at the center for the center of mass eso you get there eso for the first part, the weight A b So that's that. Let's be. And this is a So the weight or the mass of the clump. Uh, most of the clump it's going to cause the system to rotate. So So this right here gives you the movement of the clamp, which is the force on the way. That's are where r is the radius of the circle. So that is going to be equal to the in Asia provided by the mouth of the hoop. Um, so for the most of the who, the a celebration of that will be, uh a I like this. That is a A But this will be the acceleration due to the mouth of the hoop then this is the in this year from the hoop. So and then for the clump, you have the same idea. Um So like I said for the clump, there are two components of the acceleration wanted exploration one of the wind direction. And so you can see this for the clamp for the Trump. So the first two temps first two terms is for the group. In the last two tens will be for the claim. Wake up. But we have been told in the question that m sub taped. So we've been told that m sub age because three I am so be so I can do some substitution is to get everything in terms off m b. I'm gonna have, um be Jesus. MBT is just the way. Uh, that should be good to for that should be quite so image will be. Try and be. So have three b r squared Alfa because I have another one. No, three. I don't Okay. Our squid offer must be Earth with Alfa. That's a B r squared alpha. So MD g r the if you add everything up. Uh huh. Very good. Eight b r squared Alfa e got one are on the left. 200 rides council one out. I can, counselor the MBS I got g. We got to a are also so after Because one of eight. Uh, so you are with us for the first part for the second part with the people. So, like I said, the component off the acceleration in the exploration, the direction is just our Alfa, But I just are You know how far to one of a I'm g over our Listen, this councils, that gives me 18 Okay, for the white component is gonna be the same thing. Our Alfa with our times e g o r this council that wonderful g. So those are the components of the solution of that will be there for this question. Uh, thank you very much.

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Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek

Vector Mechanics for Engineers: Statics and Dynamics

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