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.
The Attempt at a Solution
working so far,
dv/dt= r*angular acceleration(al)
dv/dv=t*r/I i=moment of inertia
unable to complete the proof.