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CIE Further Maths Moment of Inertia

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    Hey guys, I really need your help here. I tried calculating the MI of the object by first summing the sphere's and the particles about the axis C, and then moving both of them to the axis O. by parallel axis theorem it would look like
    [M(4a^2) + 2(3M)(2a)^2/5] + 4M (a^2)

    which gives me (64Ma^2)/5. What am I missing? Isn't this method valid?

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    Also, I notice that the marking scheme for part (i) is kind of weird. Why did the "3" become "6" all of a sudden after the approximation?

    Please help. Thank you.
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    (Original post by johnconnor92)

    which gives me (64Ma^2)/5. What am I missing? Isn't this method valid?
    Axis C is not the centre of mass of sphere and particle combination, so you can't apply the parallel axes theorem on the combined mass.

    Also, I notice that the marking scheme for part (i) is kind of weird. Why did the "3" become "6" all of a sudden after the approximation?
    The first equation in answer to part (i) is spread over two lines, with two terms in all, each containing -3...., hence on addition -6.
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    (Original post by ghostwalker)
    Axis C is not the centre of mass of sphere and particle combination, so you can't apply the parallel axes theorem on the combined mass.
    Why not? In what cases, then, am I able to apply parallel axes theorem on composite objects?
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    (Original post by johnconnor92)
    Why not? In what cases, then, am I able to apply parallel axes theorem on composite objects?
    When you know the centre of mass. Check out the parallel axes theorem, it doesn't work on any old parallel axes.
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    (Original post by ghostwalker)
    When you know the centre of mass. Check out the parallel axes theorem, it doesn't work on any old parallel axes.
    So I can only apply the parallel axes theorem if I first find out the centre of mass of the two objects (which is somewhere below O)?
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    (Original post by johnconnor92)
    So I can only apply the parallel axes theorem if I first find out the centre of mass of the two objects (which is somewhere below O)?
    If you're working on the combined masses together, then yes.


    Which is why the mark scheme works on the individual components.

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