Two discs of moments of inertia I_(1) and I_(2) about their respective axis (normal to the disc and passing through the centre) and rotating with angular speeds omega_(1) and omega_(2) are brought into contact face to face with their axes of rotation coincident. Calculate (i) angular speed of the two disc system (ii) Show that K.E. 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 of energy?Take omega_(1)neomega_(2)

Two discs of moments of inertia I_(1) and I_(2) about their respective

1.	Two discs of moments of inertia I_(1) and I_(2) about their respective axis (normal to the disc and passing through the centre) and rotating with angular speeds omega_(1) and omega_(2) are brought into contact face to face with their axes of rotation coincident. Calculate (i) angular speed of the two disc system (ii) Show that K.E. 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 of energy?Take omega_(1)neomega_(2)
Answer» Solution :(i)`OMEGA=(I_(1)omega_(1)+I_(2)omega_(2))/(I_(1)+I_(2))` (ii)This loss must be due to FRICTION in the CONTACT of the two discs. Note that angular momentum is CONSERVED as torque due to friction is only an internal torque