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Momentof inertia and center of mass

  1. Dec 28, 2009 #1
    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 !!!)
     
  2. jcsd
  3. Dec 28, 2009 #2
    Re: momentof inertia and center of mass!!!

    and also why did he make it integration( x dm)/M it seems tome as as mass in changing, but mass is constant for this particles!!and even dont we get the constants out of integrtion soit would be xcm=x* integration(dm)/M so it would be 1=1!!!
    and also in I=intefration(r^2 dm) why did he only change mi to dm and not also r^2 i mean he made the r is equal for all mass particles!!
     
    Last edited: Dec 28, 2009
  4. Dec 28, 2009 #3

    Doc Al

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    Staff: Mentor

    Re: momentof inertia and center of mass!!!

    I = mr2 is true for a point mass, where r is the distance from the axis of rotation.
    No. In general it's not true that I = mR2 for a rigid body. It would be true if all the mass is at the same distance from the axis.
    Careful. Σ(xi*mi) ≠ Σ(xi)*Σ(mi), except in special cases.
     
  5. Dec 28, 2009 #4
    Re: momentof inertia and center of mass!!!

    so r is a function in terms of variable mass right!?
    like when i say impulse is integration(f dt) so that means as time chnages the force changes ,soin inertia it means as mass changes!!? the r changes!
     
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