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Actually what i want to know is when we are dealing with conservation of angular momentum about a stationary point (wrt. an inertial frame) we just check that whether the net torque is zero or not. But what if the point is moving? Do we have to consider torque due to pseudo force?

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Yes. If you are in a non-inertial frame, then there are fictitious forces that appear that are directed through the center of mass.

If those forces are ignored, you're going to get odd results. Imagine a horizontal bar in free fall. Consider the torques about the left end of the bar. The only force on the bar is gravity, so you might assume a clockwise net torque exists. But because the left end of the bar is accelerating downward, there is a fictitious force upward on the center of mass. This exactly cancels the torque from gravity and (as expected) the bar does not rotate.

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