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Problem 108 Easy Difficulty

Gear $C$ has a mass of 5 kg and a centroidal radius of gyration of $75 \mathrm{mm}$. The uniform bar $A B$ has a mass of $3 \mathrm{kg}$ and gear $D$ is stationary. If the system is released from rest in the position shown, determine ( $a$ ) the angular acceleration of gear $C,(b)$ the acceleration of point $B$

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Video Transcript

hello friends As soon they figure the mosque off. The Garci is given 5. 50. Radius is 100 millimeters, that is 0.1 m. Sent rattle. Radius operation is 75 millimeters, 1075 m attached to the road. Maybe at the point having the mass three on the length 200 millimeters, that is 0.2 m and Gertie is at rest because system is released from rest. Calculate angular acceleration together. See an acceleration off Trying to be let us it start solving it. First, we will discuss analytics off road and this independently So this is the diametrical view. The drop. This is the Lord a B G. It's geometrical center and this district will be half off the length of the road. That is 0.1 m. Yeah, discipline Movie downward with acceleration 0.1 in tow. Angular acceleration off the road on acceleration off the having developed why I'm doing toe Alpa. Every if the truck that the electrical figure off Discus e or Gersi acceleration off the point will be 0.2 in tow. Help a B. Yet the discus e is in contact with this Garrity. At this point, he mhm So here acceleration is 80 on this will be help. Asi this is fixed. Already given in the bush. Do you get it fixed? This is Garci. Let him make the relation. Make the relation guardian fixed. Yeah, Boring. Oh, for quite e. All right. Off Gersi Acceleration downward. Presidential Baby Europe. But we can define acceleration off. So the acceleration off the let's acceleration off with respect to be point, this is acceleration off the international direction acceleration off the Indonesian direction. This value is given zero. This we have measured point to Alpi, baby. Quite one fine to see. So from here you will get Alfa A It's cult toe half off. Help us. Is this relation we have established? No, We have to discuss the dynamics off Gersi. But we will draw the free body diagram are Garci be point here. The reaction is bx on the right. The weight will act along this direction. It is in contact with fixed, gassy at any point. So here the reaction is you. It is rotating. Then I think in tow. Empathy. No calculating moment off. Fourth, about three point. That must be heroes. The human right to in tow. Quite one is called toe. I see in tow Help Asi So you will get Moment of inertia is and three in two cases Quest and L party Mass is given. Fight radius operation off. Discuss e is 107 place. So you will get reaction to baby. Quite 281 who fight and 40 the city question toe free body diagram Part Barbie and Gersi Fpd off but a V and Gersi. This is a point. Here's the reaction. Is apes on a fight? This is the center off most of the r A V. Yeah, it's a bit, um avian toe developed. This is the center of the disc. Here's a way off the gas even act at any point. The reject, too. Here, baby. I see. In tow l party I A b in tow l five e no, for part eight moment up For about eight point, we will analyze. It would be Wait a V in tow. This distance is quite well one way off. See, in 2.2 que into 23 mark off a V into its acceleration. We already we have sown in the arugula I A B and to Alpine baby mark off the Gersi into its acceleration At any point, I seem toe help us the no substituting develop off All parameters are given. No, but it would be a tonight the into G. What? What? Five into g and try to you already We have calculated. Yeah, no, we will substitute later on months off every three white, one in tow, al five e And quite well, one white 12 or three and tow. Find two square moment often into the road. Al five, five and 2.2. And for every 2.2 minus five in tow Moment. Often it's off the disk, see as party. So yeah, after solving this equation can be written as but by three into G minus quietly And you already we have No, it is from equation to you may write it is white 2815 l party while to food Alfa heavy on al five half off. Help Asi minus 50 28125 l party From here Al Farsi, you will be named Egypt 72 536 and Contra provide direction. Unit is really in for second square so this would be the answer off first part. Now we have to calculate acceleration off the point that already we have calculated on Libya to substitute w so acceleration off people, baby, find two in tow. Alfa Evie on Alfa A V is AL party by two. 72.36 divided by So you will get acceleration off the point to be they went 0.24 m per second squared and downward direction. Direction Already we have seen in the Niagara. That's all for it. Thanks for watching it.

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Vector Mechanics for Engineers: Statics and Dynamics

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Video Transcript

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

Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Andy Chen

Marshall Styczinski

Jared Enns

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Andy Chen

Marshall Styczinski

Jared Enns

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Andy Chen

Marshall Styczinski

Jared Enns

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

Vector Mechanics for Engineers: Statics and Dynamics