Answer:
Part(a): The final angular velocity is
Part(b): The ratio of the rotational energies is ,showing the the energy of th system will decrease.
Explanation:
Part(a):
If '' be the moment of inertia of an object and '' be its angular velocity then the angular momentum '' of the object can be written as
If '' and '' be the moment of inertia of the two cylinders and '' and '' be the initial angular velocity of the cylinders and '' and '' be their respective final angular velocity, then from conservation of angular momentum,
Given, . From the above expression
Part(b):
Initial kinetic energy
and Final kinetic energy
Substituting the value of ,
The above expression shows that the ebergy of the system will decrease.