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!

U.S. Physics Olympiad F=ma 2008: Problem 12

  1. Jan 3, 2010 #1
    12. A uniform disk rotates at a fixed angular velocity on an axis through its center normal to the plane of the disk, and has kinetic energy E. If the same disk rotates at the same angular velocity about an axis on the edge of the disk (still normal to the plane of the disk), what is its kinetic energy?
    (a) 1/2E
    (b) 3/2E
    (c) 2E
    (d) 3E
    (e) 4E

    Answer: D

    Relevant Equations: KE= 1/2 I x w^2, I=MR^2

    Attempt at Solving: Io=MR^2, In=4MR^2, thus KE=4 (1/2 I x w^2)= 4E

    Can someone please explain why the answer is 3E? I really appreciate your assistance! Thanks!
     
  2. jcsd
  3. Jan 3, 2010 #2

    rl.bhat

    User Avatar
    Homework Helper

    Hi Rittted, welcome to PF.
    Moment of inertia of a uniform disc about an axis through cm perpendicular to the plane is 1/2*M*R^2.
    Using theorem of parallel axis, you can find the moment of inertia about an axis on the edge of the disk.
     
  4. Jan 3, 2010 #3

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Note that for a uniform disk, I = (1/2) m r^2, not m r^2.

    Furthermore, the parallel axis theorem may come in handy.

    Note that the kinetic energy is linear in I ([itex]E = \tfrac{1}{2} I \omega^2[/itex]) so you only need to show that [itex]I = 3 I_\mathrm{cm}[/itex], where I is the moment of inertia about the axis on the edge, and [itex]I_\mathrm{cm} = \tfrac{1}{2} m r^2[/itex]
     
  5. Jan 3, 2010 #4
    Thanks for all of the help guys! I really appreciate it!

    So I= 1/2mr^2 + mr= 3/2mr^2=3I

    and

    KE= 3E

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




Similar Discussions: U.S. Physics Olympiad F=ma 2008: Problem 12
  1. Physics F=ma Help (Replies: 2)

Loading...