Two discs having moment of inertias `I_(1)andI_(2)` about their axes passing through their respective centres and normal to their surfaces are rotating with angular speeds `omega_(1)andomega_(2)` respectively. They are brought into contact face to face with their axes of rotation coinciding with each other, what is the angular speed of the two discs system?

Options

A. `(I_(1)omega_(1))/(I_(1)+I_(2))`
B. `(I_(2)omega_(2))/(I_(1)+I_(2))`
C. `(I_(1)omega_(1)+I_(2)omega_(2))/(I_(1)+I_(2))`
D. `(omega_(1)+omega_(2))/(I_(1)+I_(2))`

Answer

C

Explanation

Here the law of conservation of angular momentum is applicable because the external forces of gravitation and their normal reaction act through the axis of rotation and do not produce any torque. Thus applying the law of conservation, we get
`I.omega=I_(1)omega_(1)+I_(2)omega_(2)`
or `omega=(I_(1)omega_(1)+I_(2)omega_(2))/(I)`
or `omega=(I_(1)omega_(1)+I_(2)omega_(2))/(I_(1)+I_(2))`
This gives the angular speed of the system after contact.