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Math Help - moment of inertia by calculus

  1. #1
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    moment of inertia by calculus

    F(z)=4|z-1-2i|^{2}+13|z-4-5i|^{2}+12|z-2-7i|^{2}+23|z-6i|^{2}
    we have to minimize or maximize F(z).can we do this question by calculus.
    actual question was
    imagine that you have 4 bodies each of mass 4, 13, 12, and 23 units located at (1,2) ,(4,5) , (2,7), and (0,6)
    we are interested in finding the point about which the moment of inertia of the system is minimum.
    (the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I =m r^2.
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  2. #2
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    Re: moment of inertia by calculus

    Quote Originally Posted by ayushdadhwal View Post
    F(z)=4|z-1-2i|^{2}+13|z-4-5i|^{2}+12|z-2-7i|^{2}+23|z-6i|^{2}
    we have to minimize or maximize F(z).can we do this question by calculus.
    actual question was
    imagine that you have 4 bodies each of mass 4, 13, 12, and 23 units located at (1,2) ,(4,5) , (2,7), and (0,6)
    we are interested in finding the point about which the moment of inertia of the system is minimum.
    (the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I =m r^2.
    the axis of rotation that minimizes the rotational inertia will have to pass through the system's center of mass ... and parallel to the the z-axis, I do believe.
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