|
So there's test tomorrow and I'm studying over the worksheet n stuff... some questions that need to be addressed, need your help O mighty team liquid! So here it goes:
First question solved, for those who still wish to see it, click spoiler. + Show Spoiler +#11) The moment of inertia of a solid cylinder is I = 1/2 mR^2. You have a cone of bas radius of r and height of d, and r = d/3. Find the moment of inertia for the cone along the axis of height. picture^ So I did this: I = 1/2 m r^2 dI = 1/2 r^2 dm then m = 1/3 * q * pi r^2 * d d=3r so m = q * pi r^3 dm = 3*q*pi*r^2 dr plug that in dI = 3/2 pi q r^4 dr integrate I = 3/10 pi q r^3 r^2 since (pi q r^3) is mass, plug mass back in I = 3/10 m r^2 and that's the correct answer on the answer sheet. However, if you try to integrate from scratch, you'll have something along the line of I = m r^2 dI = r^2 dm when you repeat this process(set up m equation, do dm = blah dr, plug that in, integrate) you still get an answer but it's twice of the correct answer you get I = 3/5 m r^2 What is wrong? I know intuitively that when you're using the first method you're unintentially integrating a whole bunch of little cylinders but how does that make sense? and when you're doing the second method instead of integrate little cylinders you're integrating hoops rather than cylinders(I think?) What is wrong in the second method and why does the first method works by taking the existing cylinder moment of inertia equation and work from there? Thanks!
second solved also [: + Show Spoiler + Second question is: When you integrate for moment of inertia, I, you normally start out with some general I equation such as I = r^2 * m you then take derivitive of both side: dI = r^2 * dm. My question is instead of dI = r^2 dm, why not use dI = 2mr dr instead? Is it entirely arbitary or does choosing dm(then substituting dm back in terms of dr) has a good reason behind it? For instance, when you integrate I of a thin rod rotating on one end(like a hinge), you do dI = r^2 dm, then: m = q * A * r (q is the density, A the cross area, r the length) dm = q A dr plug back in you get: dI = r^2 q A dr integrate you get I = 1/3 m L^2
but if you use dI = 2mr dr, then m = q * A * r plug back in you get dI = q A l * 2r dr
Ah I see... you're not expressing l in term of r, l is actually a function of r so you need to plug that in some later time...
PS more questions would probably come, I'll keep them comming.
|
so, do you ever read the front page of teamliquid?
|
Someone didn't read LiquiSpook this week!
Time to call on the Democratic People's Republic of the Mani
|
Crusade against Homework Threads
* I address you tonight not as the Editor of LiquiScoop, not as a member of the TL.net staff, but as a citizen of humanity. We are faced with the very gravest of challenges. We call these threads "Homework Threads" - the end of all productive General Forum activity. And yet, for the first time in the history of the forum, users have the wit and skill to prevent their own mental extinction. All of you reading with us tonight need to know that everything that can be done to prevent this plague is being called into service. The forum thirst for excellence, knowledge (google & wikipedia); every step up the ladder of video technology (youtube); every adventurous reach into our hard drives (random pics); all of our combined will and imaginations; even the flame wars that we've fought have provided us the tools to wage this terrible battle. Through all of the chaos that is our General Forum history; through all of the wrong and the discord; through all of the pain and he suffering; through all of our times, there is one thing that has nourished our souls, and elevated our forum above its origins, and that is our courage. The dreams of the entire TeamLiquid userbase are focused tonight on our brave anti-HW Thread warriors traveling into those threads. And may we, members of the General Forum, see these events through. Nazgul speed, and good luck to you.
* We have won our first battle, here. The thread has been closed, the evil creator banned. This glorious victory will undoubtedly be recorded in the annals of General Forum history and we thank the Democratic People's Republic of the Mani for being our unwavering ally in our darkest hour. But the war still rages, and it's not a matter of if the next HW Thread appears, but when. We will be ready.
You mean that? I actually think the intellegence of TL can be greatly appreciated by doing some good physics/math threads, and this isn't some stupid "OMG how do you integrat xdx" problem. I don't think blindly shutting down all homework threads is a bright idea because most of these threads actually stimulates intellegent discussions. Personally I think ppl like bigballs or bill actually enjoys replying to these threads for the sake of enjoyment, correct me if I'm wrong though.
|
the difference is he actualy does the work himself and has an actual question aside from
"do my homework for me" dont be so quick to jump on the bandwagon
|
On November 01 2006 22:52 Dknight wrote: Someone didn't read LiquiSpook this week!
Time to call on the Democratic People's Republic of the Mani
He isn't making a homework thread, he's already done the homework and just wants some insight into a pecurliarity he can't sort out.
I think that after this weeks liquiscoop some have adopted the "LOZL WE'RE GONNA OWN THIS THREAD" attitude because they are following the masses and probably feel a sense of "coolness" from it (I can't explain it very well).
|
I = mr^2 is for hoops. I think that's what's giving you trouble.
If you're trying to break the cylinders themselves into hoops, you still have to integrate the hoops with respect to r to get the cylinders, and then proceed from cylinders to your cone. (The cone is solid.)
|
On November 01 2006 23:11 LeoTheLion wrote: I = mr^2 is for hoops. I think that's what's giving you trouble.
If you're trying to break the cylinders themselves into hoops, you still have to integrate the hoops with respect to r to get the cylinders, and then proceed from cylinders to your cone. (The cone is solid.) So you're saying that the 2nd method instead of integrate a whole bunch of solid discs for a good solid cone, I intergrated a whole bunch of hoops so I really ended up with a extremely thin hollow cone. haha yeah that makes sense. Thanks~ -much love -evan
O to skyglow1, I think the word you're looking for is "band wagon"
|
Braavos36362 Posts
Yes, to clarify, if you actually have a homework question and you're not randomly being lazy and asking for answers, its OK to post a thread about it.
|
Something like that. =)
Ty for the physics fun.
|
Braavos36362 Posts
|
On November 01 2006 23:01 Coagulation wrote: the difference is he actualy does the work himself and has an actual question aside from
"do my homework for me" dont be so quick to jump on the bandwagon
|
On November 01 2006 23:16 evanthebouncy~ wrote:O to skyglow1, I think the word you're looking for is "band wagon"
Yes T_T
|
On November 01 2006 23:17 Hot_Bid wrote: You will be spared.
|
On November 01 2006 23:17 Hot_Bid wrote: You will be spared.
this timeO_O
|
This one is definitely different. For one, the majority of educated people won't find it easy/obvious. And it's actually an interesting problem to work out. Rotational physics is annoyingly difficult.
|
|
|
|