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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?

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?


 

Grade:11

2 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
10 years ago

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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vikas askiitian expert
509 Points
10 years ago

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 .....

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