Assume that the arbitrary-shape object shown has a torque applied at the black X with a circle, and is free to rotate about the X axis. Assume that the object is also constrained by a pin at this torque input point, parallel to the X-axis. The CG of the object is the blue plus sign, and there is an otherwise uniform mass/density distribution. Ignore gravity.
When torque is applied, is there a reaction moment/force created, acting on the constraint pin, simply from the inertia of the body being rotated (effective from the CG point, about the x-axis, against rotation)?
Or put another way, is there a constant tendancy of the object to want to naturally rotate about its CG point (instead of its constrained point), that creates a constant moment against the direction of rotation, about the CG, that acts as a force on the constraint pin?
And would such a moment exist only during acceleration (during application of torque and increase of angular velocity), or would it exist at steady state too? Would such a "reaction moment" absorb or reduce any of the kinetic energy of the rotational motion?