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Linera acceleration

  1. May 4, 2008 #1
    A reel of mass M and of radius a has tape wound round its axle
    which has radius b . The tape has negligible mass. The reel is
    initially at rest on a rough horizontal table when the free end of the
    tape is pulled horizontally by a constant force T , as shown below.
    The pull T is sufficiently small that the reel does not slide.
    Show that the resulting acceleration is given by

    a=dv/dt = a(a-b)T/M(k^2+a^2)
    where V is the velocity of the centre of the reel and k is the radius
    of gyration of the reel.

    working so far,

    dv/dt= r*angular acceleration(al)
    dv/dv=t*r/I i=moment of inertia

    unable to complete the proof.
    please help
  2. jcsd
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