Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc 
has 2 kg mass and 0.2 
radius and initial angular velocity of 50 rad 
Disc 
has 4 kg mass, 0.1 
radius and initial angular velocity of 200 rad 
. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad 
) of the system is
Text Solution
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: Moment of inertia of disc 
about an axis passing through its centre and normal to its plane is 
kg 
Initial angular velocity of disc 
rad 
Moment of inertia of disc 
about an axis passing through its centre and normal to its plane is
kg 
Initial angular velocity of disc 
rad 
Total initial angular momentum of the two discs is 
When two discs are brought in contact face to face (one on the top of the other) and their axes of rotation coincident, the moment of inertia 
of the system is equal to the sum of their individual moment of inertia. 
Let 
be the final angular speed of the system. The final angular momentum of the system is
According to law of conservation of angular momentum, we get
rad 
rad 
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