Two cylinders with radii `r_(1)` and `r_(2)` and rotational inertia `I_(1)` and `I_(2)` are supported on their horizontal axles. The first one is set in rotation with angular velocity `epsilon`. The axle of the other cylinder (smaller) is moved until it touches the large cylinder and is caused to rotate by the frictional forces between the two. Find the angualr velocity of the two cylinders after slipping ceases between them.
[Hint: Consider angular impulse received by the cylinders]

Answer

`omega_(1) = (I_(1)r_(2)^(2)omega)/(I_(1)r_(2)^(2)+I_(2)r_(1)^(2)` `omega_(2) = (I_(1)r_(1)r_(2)omega)/(I_(1)r_(1)^(2)+I_(2)r_(2)^(2))`