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Of the center of mass? Xcom What &$ the %- coordinate coordinate of the center of mass? Ycom Winat @ tmey- point perpendicular to its plane and passing through ...

Question

Of the center of mass? Xcom What &$ the %- coordinate coordinate of the center of mass? Ycom Winat @ tmey- point perpendicular to its plane and passing through I the body Is set to rotate about an aris mala M, its moment of inertia will be Ikg,m?, Tha amount of work required to take the body from rest to an angular speed of 3 rad/s is

of the center of mass? Xcom What &$ the %- coordinate coordinate of the center of mass? Ycom Winat @ tmey- point perpendicular to its plane and passing through I the body Is set to rotate about an aris mala M, its moment of inertia will be Ikg,m?, Tha amount of work required to take the body from rest to an angular speed of 3 rad/s is



Answers

Center of mass, moment of inertia, and radius of gyration Find the center of mass and the moment of inertia and radius of gyration about the $y$ -axis of a thin rectangular plate cut from the first quadrant by the lines $x=6$ and $y=1$ if $\delta(x, y)=x+$ $y+1 .$

M it wants to integral begins from 0 to 6. Integral begins from 0 to 1 x plus boy lost to on the boy index Metric waas integral begins from 0 to 6 x y lost. Why true, the Reuters body. True close. Why the X from 0 to 1 in the run begins from 0 to 6. Ace Los three. Avoid this one too. Deeks. We should holds too X. Who? The void is true. Plus three defined by true thanks From 0 to 6 on it, it was to do any seven and eggs. Of course. Toe integral begins from 0 to 6. Integral begins from zero to born Willie X, Los ploy nos Go on the boy Deeks Commission Waas in the ground being instrument 0 to 6. Integral begins from 0 to 1 boy x plus y two. Now ask boy Divine Deeks. We should waas So integral begins from 0 to 6. Why? Tool based The void is true. Lost. Why three? The point is boy industry last dry, too divided by true comes little toe all the X Richard cost so integral begins from 0 to 6. Ex provided by cool lost boy divided bully six Speaks which waas iss two divided by four anos flying divided by six east from 0 to 6 It's the home support e no big calculate And why and why? Courts Entitlement begins from zero to speaks Integral begins from zero toe wall east Thanks. Plus why Post Blanc de Roy, please. She wants for integral begins from 0 to 6 Integral begins comes little toe wall X two close Eat slowly I lost. Thanks, de boy. Thanks. Wait. Can you need I think Waas toe integral begins from 0 to 6 x two No, us three Thanks. They Why did one to decks and she wants Whoa 90 nine. So export equals two and worry they appointed by em Maybe she wants to l a van divided. Thanks. Tree The label it wants to i m x devoid of boy m. We should plans to 14 Avoid the body 20 me similar? No, we calculate. I'm boy. I want it. Waas intake run begins from 0 to 6. Integral begins from 0 to 1 East to X plus boy lost long Do you, Roy Deeks? We should waas integral begin squirm is zero who speaks es three can us East. Really? Plus thanks. These admission words to ex food divided by four plus x three Doing going true from zero 26 We should wants toe 400. There's he social on the sketches. Yes. Here it is, Roy. It calls to Bon and here it is x 4 to 6.

Okay. In this problem, it's required to find the center of mass and moment off inertia about the boy eggs I y off a scene. Rectangular plate got from the first quadrant by a line X equal to six and another line. Why equal to one for a dentist? E equal tow X plus y plus one so we can start boys Kitsch X equal to six is a line cutting X X at six and the second line. Why equal to one even other line cutting y x at one. So force the quadrants. Who is asking about this region? Now we can start calculating mess so mass will be equal to integration from Ciro 21 and second Integration from 0 to 6 for our dynasty, which is X lost Boy plus one the ex Do you want equal to integration from 0 to 1 six white clothes 24. Do you? Why? Which is equal to 27 and uh, M X equal to integration from 0 to 1 and second integration from 0 to 6 for why And then it's t x plus Why plus one e x. And this is the y. Do you, Roy equal to integration from zero 21 poor boy. But deploy six. Why? Plus 24 Do you, Roy? Equal to 14 And for him off eggs. Mm, boy. Sorry. It is same integration from 0 to 1 and another integration from 0 to 6 for eggs. Except Lewis Roy. Just one. The ex knew Roy equal to integration from 0 to 1 onto employees. 18 boy plus 90 knew Roy equal to 99. So now, easily, we can kill plate export as and Malfoy over M equal to live in over three and white board as am affects over M equal to 14 over 27. Also, it is required to complete EIroy. So why? Why will be equal to integration from 0 to 1 and integration from 0 to 6 x square, X plus y plus one the ex. Do you, Roy? Which equal to integration? From 0 to 1, 216 I'll deploy. Why? Over three loss 11 over seeks, do you? Why? Which will be equal toe? 432 Thank you.

This problem covers the concept of the uh relax this serum and foreign sphere, uh foreign sphere. The moment of nursery water standing Alexis, which means this axis for this fear of a mass. M. And the radius capital. Are the moment of inertia equals The moment of fancy about the center of mass that is to upon five M. R. Square plus the mass of this fear. And to the square of the distance between the center of mars and the Kenyans Alexis. And that is our for M. R. Square. Therefore the moment of inertia about the financial excesses seven upon 5 um uh Square the services in question. Oh for another object, The moment of Tunisia about the center of mass for his fears to a .5 Um and two small r squared. That services the question too. And since these two moment of inertia equal we can right grew up 15 M. Small R squared equals 7.5 M. R squared. How we can cancel out five on both sides and capital um on both sides. So from this R equals squirreled off seven upon 2 times the radius capital are, so the release of the new sphere Must be equals two wow 1.87 times capital R. So if the radius is 1.87 times that it is, then the moment of nasa about its central Alexis is a cuba into the moment of inertia of a another sphere with a radius capital large About 10" Alexis.

The moments M. Um it's equal to DNC. Girl From -1 to 1. You have X. Squared to one of white bloods one the white the eggs. And this is equal to negative integral from negative 1- one. You face integrate with respect to why. And that's gives us Eggs to the power for divided by two bloods X squared -3 divided by two. The it's and this is equal to 32. 32 divided by 15. Okay so our movements about the X. Axis. M. X. It makes mm X. Is equal to and see you girl from 1 -1: one. You have X. Squared one. Why? Y plus one B. Y. The eggs. And this is because too negative 11 I have five divided by six Minour takes the power six divided by three -X. The powerful divided by three D. X. And this is equal to 48 divided by 35. And movements about why M. Y. Then why it's the cold too. I antigua Against him. Once a one X. Squared one. We have AIDS. Why applies one B. Y. The eggs. And this is equal to We see once one They have three eggs divided by two minus extra power five divided by two. My next ex cube the X. And this is equal to zero. So to find the center of maths. We have eggs bam eggs bear. Which is M. Why divided by M. And this is equal to zero. And why wiper? It's a call to M. X. Divided by am. And this gives us night divided by food scene. So in Asia to find a in Asia about the why I set is going to be the integral from negative 1 to 1 X. Grade one. I have x. squared white glass one the boy the S. And this is going to be equal. So thank you for a negative 1-1. We have three X squared divided by two -X. to the power five Next to the Power six. So this is true X to the power six provided by two minus X to the power for the eighth. And this is equal to 16 divided by 35. So I wish you our radios are y It's equal to the square roots of why Why divided by mm. And this is going to be equal to the square roots of three divided by forward scene. He's our finer answer. So we have we have the radios, the movements then our center of march. So a center of mass, center of mass. That's X bar wiper is going to be equal to zero nine divided by food scene. This is the center of mars. Yes and I radius here. That's all.


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