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!

Homework Help: Moment of inertia of a solid

  1. Jun 13, 2005 #1
    How do I find the moment of inertia of a solid formed by rotating the curve of y=sinx about the x-axis in the interval [0, pi]?

    I've tried to set up integrals by summing up cylinders parallel to the y-axis but to no avail.
  2. jcsd
  3. Jun 13, 2005 #2


    User Avatar
    Homework Helper

    I'm assuming it's the moment of inertia of the solid about the x-axis that the question is asking for.

    Let the volume density of the solid of revolution be [itex]\rho[/itex]. Then a cylindrical element of mass [itex]dm[/itex] is defined by [itex]\rho \pi y^2 dx[/itex]. The moment of inertia of that element about the x-axis is defined by [itex]\frac{1}{2}y^2dm = \frac{1}{2}\rho \pi y^4 dx[/itex]. Substitute [itex]y = \sin x[/itex] and integrate over the required bounds and you have the answer. To remove the [itex]\rho[/itex] term and leave your answer purely in terms of the total mass [itex]M[/itex], just calculate the volume of revolution [itex]V[/itex] the usual way and put [itex]\rho = \frac{M}{V}[/itex].
    Last edited: Jun 13, 2005
  4. Jun 13, 2005 #3
    Yeah, that worked!

    What I did was EXACTLY the same as your method, except I multipled dm by x^2 instead of y^2. Oops.. :shy:

    Thank you. :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook