Can internal forces change the angular velocity of the system?

If the system is changeable, then under the action of internal (or external) forces, its individual points can move away from the axis, which causes an increase in the moment of inertia, or approach the axis, which will lead to a decrease in the moment of inertia. But since lw = const, then with an increase in the moment of inertia, the angular velocity of the system will decrease, and with a decrease in the moment of inertia, it will increase. Thus, the action of internal forces can change the angular velocity of rotation of the system, since the constancy of L does not mean the constancy of w in general.

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