If there is no external force acting on a non-rigid body which of the following quantities must remain constant?

Let L be the Angular momentum.

Then

External torque

When external force is zero, , that means

This condition becomes true when, L remains constant because differentiation of a constant becomes zero.

Hence, angular momentum, L remains constant if external torque is zero

Similarly,

Linear momentum p-

External force,

Hence

P remains constant if external force is zero

Hence, in the absence of external forces, angular momentum and linear momentum of system is conserved.

A change in Kinetic Energy can be seen as in case of inelastic collision.

Similarly, moment of inertia may also change in this case.