1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Moment of inertia of a sphere

  1. Jun 5, 2016 #1
    I know the moment of inertia for both a solid sphere and a hollow sphere is , but my teacher has derived a moment of inertia of the sphere but am not sure about what axis she was deriving it , and she got this answer 3/5 MR^2
     
  2. jcsd
  3. Jun 5, 2016 #2
  4. Jun 5, 2016 #3

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I also think that there must be a mistake in her derivation. Do you have it? Do you agree with all the steps?
     
  5. Jun 5, 2016 #4
  6. Jun 5, 2016 #5

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Oh! It is clearly wrong. I hope a teacher did not do that in a class!!
     
  7. Jun 5, 2016 #6
    I want to show you the paper on my notebook but I dont know how to send a pic here
     
  8. Jun 6, 2016 #7
    Now I understand , it has turned out that she meant the moment of inertia of the center of sphere and I thought it were the moment of an axis passing through the center , just because she hasn't specified clearly what she meant , thank you everyone :)
     
  9. Jun 6, 2016 #8
    How could we calculate the moment of inertia of a sphere , cut into half by the xoy plane ,, its supposed that moment of ineria about the xy and zy axes is zero , i want to know why
     
  10. Jun 6, 2016 #9

    kdv

    User Avatar

    But what does that mean exactly? There is no way to make a sphere rotate in such a way that it will have that moment of inertia, so it is actually a completely unphysical result. That's why it is never quoted as a moment of inertia of a sphere.
     
  11. Jun 6, 2016 #10

    cnh1995

    User Avatar
    Homework Helper

    Do you mean a hemisphere? Solid or hollow?
     
  12. Jun 6, 2016 #11

    jbriggs444

    User Avatar
    Science Advisor

    The "xy" axis is a synonym for an axis in the z direction? So if the moment of inertia about this axis is zero, every point within the sphere must be somewhere on the z axis.

    The "zy" axis is a synonym for an axis in the x direction? So if the moment of inertia about this axis is zero, every point within the sphere must be somewhere on the x axis.

    It follows that every point within the sphere must be at the intersection of the x and z axes. i.e. at the origin. Well, yeah, that moment of inertia is fairly easy to calculate.
     
  13. Jun 6, 2016 #12
    I haven't sensed a physical meaning to it yet in my head , but there's a formula that states tge summation of moments of inertia wrt x-axis ,y axis and z axis , respectively is equal to two times the moment of inertia at the origin . I think so .. Unfortunately i dont have enough time to understand this lesson we've taken lately , my exam is after tomorrow , but am sure that she wrote this title "moment of inertia w.r.t a point"
     
  14. Jun 6, 2016 #13
    A solid sphere
     
  15. Jun 6, 2016 #14
    They are not given zero to us , they should be proved by calculation , but am not knowing how
     
  16. Jun 7, 2016 #15

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

    Why so complicated? I guess we assume a homogeneous sphere of density ##\rho=3m/(4 \pi R^3)##. The rotation axis is through the center (all other cases can be evaluated with Steiner's law). Take spherical coordinates and the rotation axis around the polar axis. Then we have
    $$\Theta=\rho \int_0^{2 \pi} \mathrm{d} \varphi \int_0^{\pi} \mathrm{d} \vartheta \int_0^{R} \mathrm{d} r r^2 \sin \vartheta r^2 \sin^2 \vartheta = 2 \pi \rho \frac{R^5}{5} \int_{-1}^1 \mathrm{d} u (1-u^2) = \frac{8\pi }{15} \rho R^5=\frac{2}{5} m R^2.$$
    In the last step, I've substituted ##u=\cos \vartheta##, ##\mathrm{d} u =\mathrm{d} \vartheta \sin \vartheta##, ##\sin^2 \vartheta=1-u^2##.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Moment of inertia of a sphere
Loading...