1. Not finding help here? Sign up for a free 30min 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!

Metal disk problem!

  1. Nov 29, 2012 #1
    1. The problem statement, all variables and given/known data

    A uniform metal disk (M = 8.21 kg, R = 1.88 m) is free to oscillate as a physical pendulum about an axis through the edge. Find T, the period for small oscillations.

    2. Relevant equations

    [itex]I = mr^{2}/4[/itex]
    [itex]T = 2\pi √(I/mgd)[/itex]

    3. The attempt at a solution

    I combined the formula together to get:

    [itex]T = 2\pi √((mr^{2}/4)/(mgr))[/itex]
    [itex]T = 2\pi √(r/(4g))[/itex]

    But the answer is incorrect
     
  2. jcsd
  3. Nov 29, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    How did you arrive at this result?
     
  4. Nov 29, 2012 #3
    I am thinking that I need to use the moment of inertia of the disk.
     
  5. Nov 29, 2012 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Of course you do, but that's not the correct formula.
     
  6. Nov 29, 2012 #5
    Then, it's something like I = mr²/2, rotating to its center. However, the disk oscillates through its edge.

    I am not sure which path to go for...
     
  7. Nov 29, 2012 #6

    Doc Al

    User Avatar

    Staff: Mentor

    Right.
    Use the parallel axis theorem. (Look it up!)
     
  8. Nov 29, 2012 #7
    Hm.. By the Parallel Axis Theorem, I would assume that:

    [itex]I = I_{center} + md^{2}[/itex]
    [itex]I = mr^{2}/2 + mr^{2}[/itex] [Since the disk rotates about an axis through the edge, we must add the inertia by mr². r is the distance between the center and the edge of the disk.]
    [itex]I = 3mr^{2}/2[/itex]

    Is that how I approach this? Let me know where I go wrong. Otherwise, I can just plug and chug this expression:

    [itex]T = 2\pi √((3mr^{2}/2)/(mgr))[/itex]
    [itex]T = 2\pi √(3r/(g))[/itex]
     
  9. Nov 29, 2012 #8
    Nvm. My answer is right. Thanks for your help by the way!
     
  10. Nov 29, 2012 #9

    Doc Al

    User Avatar

    Staff: Mentor

    Good! :approve:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Metal disk problem!
  1. Spinning Disk Problem (Replies: 2)

  2. Two Metal Disks (Replies: 2)

  3. Rotating disk problem (Replies: 25)

Loading...