## El_Psy_Congroo!! 3 years ago Q

1. El_Psy_Congroo!!

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2. El_Psy_Congroo!!

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3. RolyPoly

r(lambda) d(theta)?

4. El_Psy_Congroo!!

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5. RolyPoly

R^3 (lambda) d(theta)?

6. El_Psy_Congroo!!

correct ... the shape of ring goes all the way round to 360 and varies with d(theta) ... so what do we do?

7. RolyPoly

You mean....?

8. El_Psy_Congroo!!

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9. RolyPoly

whole ring? length = r theta I = r^3 theta (lambda)

10. El_Psy_Congroo!!

no ... this varies with theta ... so we integrate it along 0 to 2 Pi

11. El_Psy_Congroo!!

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12. RolyPoly

I think I got it..

13. El_Psy_Congroo!!

so what is the final answer?

14. RolyPoly

(lamda) R^3 (2 pi)

15. El_Psy_Congroo!!

yep .. what would (lamda) (2 pi) R = ??

16. RolyPoly

M?

17. RolyPoly

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

18. El_Psy_Congroo!!

yeah the moment of Inertia of ring is MR^2

19. El_Psy_Congroo!!

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20. El_Psy_Congroo!!

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21. RolyPoly

Wait, surface / unit area? What's that?

22. El_Psy_Congroo!!

sorry ... mass per unit area ... typo.

23. RolyPoly

Mass = sigma (area) = sigma (pi)[(r_2)^2-(r_1)^2) = sigma (pi) (dr) (2r+dr) Have to go now. I'm sorry!

24. El_Psy_Congroo!!

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