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Aakash Dutta Grade: 11
        

how to find the moment of inertia of a disc of variable density


for ex -


find the MOI wrt Centre of a disk of surface density which varies as (A + Br) where r is distance from centre Total radius - R?


 

6 years ago

Answers : (2)

AKASH GOYAL AskiitiansExpert-IITD
419 Points
										

Dear Aakash


I=∫(dm)r2


you have to take an element and find dm for that


take ring of width dr at a distance r from the centre


area of elemental ring=2∏rxdr


mass of this ring= dm= (A+Br)2∏rxdr


I=∫(A+Br)2∏r3 dr limits from 0 to R


just intrgrate


I=2∏(AR4/4 + BR5/5)


 


All the best.                                                           


AKASH GOYAL


AskiitiansExpert-IIT Delhi


 


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6 years ago
vikas askiitian expert
510 Points
										

take elemental ring of r & thickness dr ...


mass of this ring is dm = (A+Br)2pirdr


moment of inertia = dmr2


now integrate this , take limit from 0 to R ...


this will give the total moment of inertia .....

6 years ago
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