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OCW Scholar - Single Variable Calculus
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|dw:1350922648157:dw|
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r(lambda) d(theta)?

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Other answers:

|dw:1350923517490:dw|
R^3 (lambda) d(theta)?
correct ... the shape of ring goes all the way round to 360 and varies with d(theta) ... so what do we do?
You mean....?
|dw:1350923841372:dw|
whole ring? length = r theta I = r^3 theta (lambda)
no ... this varies with theta ... so we integrate it along 0 to 2 Pi
|dw:1350924064331:dw|
I think I got it..
so what is the final answer?
(lamda) R^3 (2 pi)
yep .. what would (lamda) (2 pi) R = ??
M?
Wait.. I was partly right.. length = r theta I = r^3 theta (lambda) One more condition there is theta = 2 pi I = r^3 (2pi) lambda
yeah the moment of Inertia of ring is MR^2
|dw:1350924842776:dw|
|dw:1350924935079:dw|
Wait, surface / unit area? What's that?
sorry ... mass per unit area ... typo.
Mass = sigma (area) = sigma (pi)[(r_2)^2-(r_1)^2) = sigma (pi) (dr) (2r+dr) Have to go now. I'm sorry!
|dw:1350925702449:dw|

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