find-the-indicated-moment-of-inertia-or-radius-of-gyration-find-the-moment-of-inertia-in-mathrmkg--3

Question

Find the indicated moment of inertia or radius of gyration.
Find the moment of inertia (in $\mathrm{kg} \cdot \mathrm{m}^{2}$ ) of a rectangular door $2 \mathrm{m}$ high and $1 \mathrm{m}$ wide with respect to its hinges if $k=3 \mathrm{kg} / \mathrm{m}^{2}$ (See Exercise 22.)

Averell Hause · Accepted Answer

so we can draw the store we have. And we have two bars. And we know that this distance here is considered out so we can consider the door to be made out of a large number of thin horizontal rods which, uh, this is an attempt that, uh, detail ing that. And, ah, with each of the length of El equaling 1.0 meters, so we can say that is there is rotating about one end. This would be the axis of rotation essentially, because when you open the door, this would this is how this is the axis about which it would rotate. We can You can see these two of these rods in this diagram, and it would simply be, ah, large number of thin horizontal rods all parallel to one another. So we can say that the moment of inertia of one of these rods would be equal to 1/3 time&#x27;s initial l squared where, um, sub I is the mass of one single rod, so we consider it for a collection of identical rods all parallel to one another. The moment of inertia of the door would then be equal to the sum of 1/3. I&#x27;m sub I l squared, which would be equal to 1/3 times the mass of the door. L squared because the sum of all of the masses of these identical rods would be equal to the mass of the door. So we can say that the moment of inertia of the door would then be equal to 1/3 times 19 0.0 kilograms multiplied by 1.0 meters quantity squared. And so the moment of the moment of inertia for the door would be equal to 6.3 approximately kilogram meters squared. This would be our final answer. That is the end of the solution. Thank you for watching.

Ahmed Ibrahim · Answer

this problem, it&#x27;s required toe plate moment of inertia about XX for a circle with the radius equal toe toe either Think, Felice Plate, you cleared I x for a dentist equal to one. Then calculate I i y And I note we can start boy needing i x So I x equal toe integration from negative to which is the radius to two and integration from negative four minus x square to route four minus x square for Why square do you? Why the yucks? So we can simply fly or solve it as integration from negative tool to two over three record full minus X squared Well, 4 3/2 DX and this should be equal to four by and from cemetery We can conclude that why is equal to Y X, which is equal to four boy, then I know he&#x27;s some off my eggs And why? Why? So it will be equal toe a boy. Thank you

Yiming Zhang · Answer

So here we&#x27;re gonna find the moment when they&#x27;re sure with respect. Why? Let&#x27;s see. Um So first we find the region. We have access from a pipe to pie and every equation we had White goes toe at the X equals two science away X squared exes from party to pie. Here we have the appointment of ex so wise from zero to there&#x27;s a positive choice. The lower ground zero in the upper about mistresses function of X, which is that&#x27;s sinus over X square, the Y. And this is with respect. Why? So we hear McCloy, we multiply X squared and I&#x27;m in trouble over this equation, we&#x27;re gonna have 1/2 times pie to two pi. And inside is where have one minus kowtowing to eggs. Here we have the X, Then the answer for that is half party

Averell Hause · Answer

party. We have a thin hoop with the radius are. And we can say that the moment of inertia, I would be equaling m k squared. And this is equaling m r squared. And so here the radius of gyration with Kay would be eagling are the radius. Here you have the moment of inertia equaling again m k squared. This would be equaling to 1/2 um, r squared plus 1/12. Um, W squared. And so here we can say that Kay, the radius of gyration would be equaling the square root of one over two r squared plus one over 12. Ah, with squared. And so this would this would be the radius of gyration with a thin hoop everythin hoop with a radius and a with. Now we have a solid cylinder where here, the moment of inertia is equal in again M k squared. And then specifically for a solid cylinder, we have 1/2 mm r squared. So here the radius of gyration is equaling. Are the radius multiplied by the square root of 1/2 for a hollow cylinder? We have I equaling m k squared, and this would be equaling 1/2 times and sometimes the smaller radius plus squared plus the larger radius squared. And so here, the radius of gyration kay would be equaling the square root of 1/2 times our sub one squared. Let&#x27;s are set to square four part E a uniform sphere. We have the moment of inertia equaling again M k squared and then specifically for a uniform sphere, we have 2/5 um, r squared. And so the radius of gyration for ah uniforms speak uniforms. Sphere would be the radius times the square root of two over five for a long rod through the center, eyes equaling again at K squared, This would be like one over 12 times. AM l squared where the radius of gyration K is now equaling oh, multiplied by one over 12 and then finally four part G and H Gene, we have a long rod through the end. This would be I equaling, encased, squared and this would be equaling 1/3 m l squared. And so the radius of gyration K is equaling l times the square root of one over three. And now we have new rectangular thin plate. This would be the moment of inertia equaling M K squared. Uh, this would be equaling 1/12 Um, times l squared, plus the length squared plus the with squared and so Okay, The radius of gyration would be equal to the square root of 1 12 l squared plus w squared. That is the end of the solution. Thank you. For what?

Ahmed Ibrahim · Answer

In this problem, you should find the center of mess and the moment of inertia about the coordinate axes which is my ex and Roy and the polar moment of inertia. Our note off, I think off a saint Wrangler plate pounded boy lines. Why equal to X and why? Equal negative X And why equal one with a dentist equal y plus one. So this is thought by sketching our curves. So first line is why equal X It should be like these. Second line is why equal negative X which is like exists then why equal one so use line cutting Why exes at one. So if we intersect these lines, we can get the at negative one at X equal negative one and this point at X equal to one and he&#x27;s asking to get the requirement for these region. So now we can start our creation with his moment equal to integration from 0 to 1 and second integration from negative white toe boy for y plus one which is our dynasty. The ex do you, Roy, which equals toe integration from 0 to 1 to y square. Last toy Deroy we cool 5/3 and em off eggs equal to same integration from the, you know, to one. And second continuation from Negative Boy to Roy for Why deploy? Why plus one dx. Do you, boy with equal to integration from 0 to 1 toe, Apply wipe or three. Plus. Why yours too? Do you worry? Yeah. This used boy the y equals 7/6 and now I&#x27;m off eggs a ma foi me? Yeah. So Emma Foy equal to integration from 0 to 1 and second degree from negative one toy for X and Dennis T y plus one d x d oi! Equal to integration from 0 to 1 equal to zero. Do you want? So am I will be equal to zero. And now we can kill Clete Export, which is a boy over m and it will be equal to zero and wild boar, which is m X over m. It will be 7/10. Also it is required to complete the moment of inertia. So starting by I X integration from 0 to 1 and from negative white Why for voice square? Why plus one which is a dynasty. The ex Do you know why Equal to integration from 0 to 1 toe. Why bore four? Must tow. I bore three. Do you? Why? Which equal to line over 10. And are you? Why is integration from 0 to 1 and integration from negative white? Why? For exits squares off. Deploy our tennis TVG y plus one the ex Do you lie? You can rewrite this portion. It&#x27;s not clear y plus one. So this will be equal to integration from this one from 0 to 1 won over three toe by two y or four plus toe or three. Dear boy, you teach equal to city over 10. Finally I know which is a Polish moment off inertia is some off I X plus y y, which will be equal to 6/5. Thank you.

Problem

Find the indicated moment of inertia or radius of…

Problem 26 Easy Difficulty

Find the indicated moment of inertia or radius of gyration.
Find the moment of inertia (in $\mathrm{kg} \cdot \mathrm{m}^{2}$ ) of a rectangular door $2 \mathrm{m}$ high and $1 \mathrm{m}$ wide with respect to its hinges if $k=3 \mathrm{kg} / \mathrm{m}^{2}$ (See Exercise 22.)

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Integration Review - Intro

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Basic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Kayleah T.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus