In the experiment of moment of inertia , torque of friction force is ignored (mainly air friction force) or drag force.
When the body rotates friction force due to air will act on body in the opposite direction of motion. It depends on the shape of the body and velocity of body. If the surface area on which air is striking is small then it's effect will be less.
Or for high speed experiment it can not be ignored because drag force is proportional to velocity.
Other force is deformation force.
The force causing deformation in the body or when a soft body rotates then it's mass will shift toward peripheral and it's moment of inertia will increase.
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