How to derive the formula for moment of inertia of a disc about an axis passing through its centre and perpendicular to its plane? Can you please explain the sams with a figure drawn?😅

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Answer 1 · 2017-05-31T16:28:37

See the proof below

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The mass of the disc is #=M#

The density is #=rho#

The radius of the disc is #=R#

We start with the definition

#dI=rhor^2dV#

#rho=M/V_(disk)=M/(pir^2h)#

#V=pir^2h#

#dV=2pirhdr#

#I=M/(pir^2h)int_0^Rr^2(2pihrdr)#

#=M/(pir^2h)*2pihint_0^Rr^3#

#=2M/r^2[r^4/4]_0^R#

#=1/2MR^2#