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!

Rotation of rigid body - wobbling

  1. May 7, 2008 #1
    When a rigid body experiences a rotation about an axis other than one of its "principal axis of rotation", it experiences a "wobble"

    I have been trying to understand why this is so (intuitively).

    Here is what I have come up with - please tell me if I have misconceptions or misunderstandings, or if I'm just full of crap :(

    I have come up with this qualitative explanation - the particles that comprise the rigid body are subject to two constraints - they must rotate about [tex]\omega[/tex], but at the same time they must stay fixed relative to each other. The latter constraint introduces the wobble when the rotation is not about a "principal axis of rotation".

    Is that a correct way of looking at it?

    A more mathematical explanation I have come up with is (tell me if any of these concepts are flawed... hopefully this makes some sense without a drawing) -

    Rigid body experiences a rotation about [tex]\omega[/tex], where [tex]\omega[/tex] is not parallel to a principal axis of rotation.

    Viewing the system from a coordinate system that is fixed with respect to the "inertial tensor" I of the rigid body,
    [tex]\omega[/tex] actually appears to rotate about a principle axis

    (imagine instead rotating the coordinate system about [tex]\omega[/tex] - [tex]\omega[/tex] effectivly rotates about a principal axis(s)).

    Therefore, because by definition

    L = I [tex]\bullet[/tex] [tex]\omega[/tex]

    coordinate system is fixed with respect to inertial mass tensor I
    so dI/dt = 0

    but [tex]\omega[/tex] is not fixed in the coordinate system so
    d[tex]\omega[/tex]/dt [tex]\neq[/tex] 0

    therefore, dL/dt = torque [tex]\neq[/tex] 0

    And this torque is responsible for the wobble.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Rotation of rigid body - wobbling
  1. Rotation of rigid body (Replies: 4)

  2. Rotation of Rigid body (Replies: 2)

Loading...