Q7.25     Two discs of moments of inertia I_{1} and I_{2}  about their respective axes (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.

              (a) What is the angular speed of the two-disc system?

Answers (1)

Let the moment of inertia of disc I and disc II be I1 and I2 respectively.

Similarly, the angular speed of disc I and disc II be w1 and w2 respectively.

So the angular momentum can be written as : 

                                         L_1\ =\ I_1 \omega_1             and             L_2\ =\ I_2 \omega_2

Thus the total initial angular momentum is :      =\ I_1 \omega_1\ +\ I_2 \omega_2

Now when the two discs are combined the angular momentum is :

                                                                     L_f\ =\ (I_1\ +\ I_2)w

Using conservation of angular momentum :

                                         I_1\omega_1\ +\ I_2\omega_2 =\ (I_1\ +\ I_2)w

Thus angular velocity is :

                                                     \omega \ =\ \frac{I_1\omega_1\ +\ I_2\omega_2}{I_1\ +\ I_2}