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Why does it require less work?

  1. Mar 25, 2010 #1
    1. The problem statement, all variables and given/known data

    Four tiny spheres are fastened to the ends of two rods of negligible mass lying in the xy plane.
    figure is illustrated below.

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    2. Relevant equations


    3. The attempt at a solution
    I see I can derive the problem using equations to answer my question.
    But here is a statement the textbook made

    In part A we are ask "if the system rotates about the y axis" whereas in part B, we are asked "rotate the system about z axis"

    In this problem, we will expect all four spheres will be revolving when it is revolve about z axis.
    How did the author come up with this statement using W-K theorem?
     
  2. jcsd
  3. Mar 25, 2010 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Let me assume that the whole construction is like a plus sign, with all spheres identical and at the same distance d to the centre.

    Let I be the moment of inertia of such a sphere around the centre (I suppose you need the parallel axis theorem and it will be something like I = Isphere + m d2, but that's irrelevant). Then when you rotate around the y-axis, only two of the spheres are moving, so you will get something like
    Itot = 2I.
    When you rotate around the z-axis, all four are moving and you have
    Itot = 4I.

    Since the work-energy theorem states that the work W is proportional to Itot, the conclusion would follow.
     
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