The two uniform discs rotate separately on parallel axles. The upper disc (radius a and momentum of inertia I1) is given an angular velocity ω0 and the lower disc of (radius b and momentum of inertia I2) is at rest. Now the two discs are moved together so that their rims touch. Final angular velocity of the upper disc is

The two discs exert equal and opposite forces on each other when in contact. The torque due to these forces changes the angular momentum of each disc. From angular impulse-angular momentum theorem, we havefa∆t = I1(ω0-ω1)----------(i)and fb∆t = I2ω2---------(ii)From eqns. (i) and (ii), we get ab = I1(ω0-ω1)I2ω2------(iii)When slipping ceases between the discs, the contact points of the two discs have the same linear velocity,i.e.,aω1 = bω2-----(iv)On substituting ω2 in eqn. (iii) we getω1 = (I1ω0)[I1+(a2I2b2)]