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For e.g.

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Here, A,B are strings. A was cut. The rod is of length l. Acceleration of center of mass = a and angular acceleration of the rod is alpha.

Now if I want to find the net torque about the point of intersection of B and the rod(which is accelerating towards the right with $l/2 sin37 \theta $), why do I have to apply a pseudo force on the c.o.m and observe it from that accelerating frame to equate net torque = $I\alpha$ (including the torque due to pseudo force)? Why can't we do it from the ground frame? why does the point about which we take the net torque and equate it to $I\alpha$ have to be non-accelerating?

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There is no reason why you cannot use an inertial frame such as the ground. You only apply pseudo forces when using a non-inertial frame.

If you do use a non-inertial frame of reference, then you have to treat pseudo-forces the same as real forces - ie you have to consider their tendency to rotate an object as well as their tendency to cause liner motion in this frame.

In an inertial frame the pseudo force does not exist, therefore it causes no torque in this frame of reference.

The torque on the rod is the same whichever axis you measure it from. Torque is provided by a couple which is two equal and opposite forces separated by a non-zero distance. Distance from any axis does not come into the definition, only the distance between the forces.

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