When no external torque acts on a system, its angular momentum remains constant. Is the statement true ? Should kinetic energ of rotation of the system remain constant ? If yes, why , and if no, why not?

Explanation

Yes, the statement is true. This is as per the principle of conservation of angular momentum, i.e.
When `tau = 0, L = I omega =` constant.
Now, `K.E`. of rotation `= (1)/(2)I omega^(2)`
`E = (I^(2)omega^(2))/(2I) = (L^(2))/(2I)`
As `L` is constant, therefore, `E prop (1)/(I)`
i.e., `K.E.` of rotation of the system shall NOT remain constant.
If moment of inertia `//` of the system increase, `K.E` of rotation `E` will decrease and vice-verse.
However, K.E. of rotation will remain constant if moment `//` of the body is maintained constant.