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Direction of instantaneous axis in rigid body dynamics

  1. Mar 9, 2015 #1
    question.jpg
    The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of
    mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass.
    These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed)
    horizontally at its rim to a massless stick, as shown in the figure. When the disc-stick system is rotated
    about the origin on a horizontal frictionless plane with angular speed w, the motion at any instant can be
    taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation
    of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the
    changed orientation of points P and Q). Both these motions have the same angular speed w in this case.
    Now consider two similar systems as shown in the figure: Case(a) the disc with its face vertical and
    parallel to x-z plane; Case (b) the disc with its face making an angle of 45° with x-y plane and its
    horizontal diameter parallel to x-axis. In both the cases, the disc is welded at point P, and the systems are
    rotated with constant angular speed wabout the z-axis.what is the direction of instantaneous axis (passing through the centre of mass in case (a) and (b).please explain all the concepts in detail.i will be highly thankful.
     
  2. jcsd
  3. Mar 13, 2015 #2

    Dale

    Staff: Mentor

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