## Transcribed Text

Attwood's machine A uniform circular pulley of mass 2m can rotate treely about Its
axis
12.2 of symmetry which is fixed in a horizontal position. Two masses m, 3m are connected by
light
inextensible string which passes over the pulley without slipping. The whole system
undergoes a planar motion with the masses moving vertically. Take the rotation angle of the
pulley as generalised coordinate and obtain Lagrange's equation for the motion. Deduce the
upward acceleration of the mass m.
362
12.5 A uniform solid cylinder cylinder of radius b. between the the two
C with mass m and In radius the motion, a rolls the on axes the rough of outer
cylinders surface of remain a fixed parallel horizontal to each upward other. vertical. Let a be Taking the angle 0 as generalised coordinate, plane con-
the
cylinder
axes
and
the
taining
is
equivalent
to
the
Lagrange's
equation
and
verify
it
energy
that
conservation
obtain
equation. the cylinder C is at rest on top of the fixed cylinder when reaction it is given force a very small
C. disturbance. Deduce that C will as a leave the fixed cylinder when 0 = cos (4/7). Is the assumption that
Initially Find, function of 0. the normal component of the exerted on
rolling persists up to this moment realistic?
12.7 A uniform ball of mass m rolls down a rough wedge of mass M and angle a, which
itself can slide on a smooth horizontal table. The whole system undergoes planar motion.
How many degrees of freedom has this system? Obtain Lagrange's equations. For the special
case in which M = 3m/2, find (i) the acceleration of the wedge, and (ii) the acceleration of
the ball relative to the wedge.

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