and 
about their respective
axes (normal to the disc and passing through the centre), and rotating with
angular speed 
and 
are brought into
contact face to face with their axes of rotation coincident.
(i) What is the angular speed of the
two-disc system? (ii) Show that the kinetic energy of the combined system is
less than the sum of the initial kinetic energies of the two discs. How do you account
for this loss in energy ? Take 
.
Answer:
(i) Let 
be
the angular speed of the two-disc system, then by conservation of angular
momentum,
or 
(ii) Initial K.E. of the two
discs,
Final K.E. of the two-disc
system,
Loss in K.E. 
Loss in K.E.
positive
quantity
Hence there is a loss of rotational K.E.
which appears as heat. When the two discs are brought together, work is done
against friction between the two discs.
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