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Rotational inertial and energy.

  1. Jul 11, 2015 #1
    1. The problem statement, all variables and given/known data
    The figure shows a rigid assembly of a thin hoop (of mass m = 0.25 kg and radius R = 0.13 m) and a thin radial rod (of length L = 2R and also of mass m = 0.25 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation?

    2. Relevant equations
    I=1/3 ML2 (rod)

    3. The attempt at a solution

    Im having trouble finding the rotational inertial of the rod and the hoop.
    for the rod im using 1/3 ML2 because its I of the rod rotating about its end.
    for the hoop i tried using its com and applying that to the formula I=MR2, where M=.25kg and R=.39m
    edit. complete
    Last edited: Jul 11, 2015
  2. jcsd
  3. Jul 11, 2015 #2
    to relate rotational inertia to angular velocity use the kinetic energy-work formula. ΔK=½ Iωf2 - ½ Iωi2.
    where ΔK = change in gravitational potential engery, because there is no other forces acting on the system.
    I=the sum of the rod and hoop, and the hoop you need to use the parallel axis theorm
  4. Jul 11, 2015 #3


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    The rod and hoop are rotating about the end of the rod opposite of the hoop, so don't worry too much about calculating the MOI about the c.g.of the combo.

    Be careful about which formula you use to calculate the MOI of the hoop about its c.g. If you are using a table of formulas, inspect very carefully which formula goes with which axis of rotation. There's two different formulas for the MOI of a hoop.

    The image of your calculations looks like you spilled something all over the paper. Try to show a little pride in your work. This stained paper suggests to your instructor that you are trying not to spend a lot of time on your work.
  5. Jul 11, 2015 #4
    My instructor will not see this, I just have to enter the correct answer into online homework website.
  6. Jul 11, 2015 #5


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    So far it doesn't look like you're getting the correct answer, are you ?

    By the way: What's the purpose of having you do homework?
  7. Jul 11, 2015 #6
    Yes, i have completed this problem. in post#2 I tried to explain how i found the answer.
    The purpose of doing homework is to learn by practice. And its worth points toward my grade.
  8. Jul 11, 2015 #7


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    I don't think J-dizzal did that.
  9. Jul 11, 2015 #8


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    Quite frankly, it's hard to tell exactly what he did. It's also not clear that the snap shot of his calculations shows his latest work, either.
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