(adsbygoogle = window.adsbygoogle || []).push({}); momentof inertia and center of mass!!!

in book of serway : he says moment of inertia of a body is m(r^2).---->(1)

is mass of the body and r is the distance of the body.

but for a rigid body we will divide into particles of very small masses so i = E(Mi * (Ri)^2)

E() is submission function to number if i Th particles.

and he says if we decrease this mi or delta m i to very small amount

so I = lim(mi->0) mi*(ri)^2 which will equal integration( r^2 dm).

SO WHAT DID HE DO IF I SOLVE THE INTEGRATION IT WILL BE I=MR^2 the same as the first equation(1) !!!!?

and also i have the same problem in center of mass

he says if we want to find x coordinate of center of mass so:

x=E(mi*xi)/M and again if we deal with a rigid body of infinite of particles it will be :

x=lim(mi->0) (mi*xi)/M = integration( x dm)/M

so what!!! if we solve this integration it will be xcm= (x* M)/M

so xcm=x (and u dont have x because x is xcm that u want to find so what did he do with this stupid integration !!!)

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# Momentof inertia and center of mass

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