Nonuniform Density Center of Mass
Determine the x-position center of mass of a horizontally oriented rod with a length of 0.65 m and linear mass density of [43 - 21 x^2 ] g/m. Want Lecture Notes? www.flippingphysics.com/center...
This is an AP Physics C: Mechanics topic.
Previous Video: Center of Mass by Integration
www.flippingphysics.com/center...
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Content Times:
0:00 Introduction
0:33 Three kinds of mass density
1:34 Translating the problem
2:19 Estimating Center of Mass
3:42 Finding Total Mass
7:10 Finding Center of Mass
8:09 Finding Our Mistake
#APPhysicsC #CenterOfMass #NonuniformDensity
Пікірлер: 35
Your videos are making me love physics. I've just used them in a high school test for the escape velocity from the center a non uniformly dense planet.
@FlippingPhysics
2 жыл бұрын
Wonderful!
I seriously love this. Real physics and comedy=Fun. It made my morning. Thank you so much!
@FlippingPhysics
3 жыл бұрын
Glad you enjoyed it!
Netflix should give you your own show
@FlippingPhysics
3 жыл бұрын
I wish…
I didn't review this before the exam day May 3rd, so I forgot how to get the integral correctly. But I remembered how to set up this integral when I just submitted the exam! TAT
Your videos ae awesome- been doing this over 30 years and I think it's great that I can still pick up something new or different from you to help my lessons be better!
Three men A,B & C of masses 40 kg, 50 kg and 60 kg are standing on a plank of mass 90 kg, which is kept on a smooth horizontal plane. If A & C exchange their positions then mass B will shift.......m Any solution?
@FlippingPhysics
3 жыл бұрын
Watching this video should help: www.flippingphysics.com/painter-scaffold.html
Thanks for helping with some last-minute review/cramming before the exam tomorrow!
@FlippingPhysics
3 жыл бұрын
Best of luck tomorrow with that _digital_ exam!
This is all fine and dandy but how would you ever know what the density function of a nonuniform object is? Is there some way to measure it? I know that question is probably out of the scope of this video but I can't find a straight answer to this simple question anywhere.
Thank you very much, i wish you had more views, there's so much effort here
@FlippingPhysics
2 жыл бұрын
Glad you appreciate it.
Amazing !!
Your videos are just amazing......
@FlippingPhysics
Жыл бұрын
Thank you so much 😀
Thank you very much!
@FlippingPhysics
6 ай бұрын
You're welcome!
Great vid
Looks great!
@FlippingPhysics
3 жыл бұрын
Thanks so much for looking it over!
Gem of a video
When doing the final integral, I just solved for lambda(lambda = total mass/total length), and used that. But, I got the first incorrect answer..wonder why that is..
Amazing!
@FlippingPhysics
3 жыл бұрын
Thank you! Cheers!
bro how do you clone 3 versions of yourself do you film them seperately?
@FlippingPhysics
6 ай бұрын
physics
Hello! What about an object that isn’t a rod... with a non uniform cross section?
@carultch
2 жыл бұрын
In any case, you select a mass element dm, that you allow to vary as a function of x. At any given x-position, dm will equal the mass of the thin slice you make, of thickness dx. Suppose we have a cone, made out of some kind of sand-filled resin, that varies linearly in density with position along the x-axis, and density of any given cross-section perpendicular to the x-axis is uniform. We are letting the x-axis be the vertical position, which is zero at the bottom. At the top of the cone, where the radius diminishes to zero, the density is rho2, and at the bottom of the cone, the density is rho1. The base radius is R, and height is H. Our cone's radius as a function of x is: r(x) = R*(H - x) The density is: rho(x) = rho1 + (rho2-rho1)*x/H Our mass element is equal to density times area times dx: dm = rho(x) * pi*r(x)^2 * dx To find total mass, integrate dm: M = integral dm M = integral rho(x) * pi*r(x)^2 * dx M = integral (rho1 + (rho2-rho1)*x/H)*(R*(H - x)) dx, from x=0 to H M =1/6*H^2*R*(2*rho1 + rho2) To find center of mass, integrate x*dm, and then divide by M: xbar = integral x*dm / M integral x*rho(x) * pi*r(x)^2 * dx = 1/12*H^3*R*(rho1 + rho2) Divide by M: xbar = 1/12*H^3*R*(rho1 + rho2)/(1/6*H^2*R*(2*rho1 + rho2)) Simplify to get result: xbar = 1/2*H*(rho1 + rho2)/((2*rho1 + rho2))
ياريت ترجمة بالعربي
I keep hearing exposition(English word)
@FlippingPhysics
3 жыл бұрын
I tried very hard to say _x-position_ very clearly, however, I fully understand why it may sound like _exposition_ 😬
@carultch
2 жыл бұрын
When I saw this video for the first time, I never once gave a single thought to the fact that x-position would sound like exposition. Now that I see your comment, I cannot unhear it. Now I'm reminded of the similarity in sound every time I see either word.