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Please consider two cases.


1)Suppose a rod is hinged, such that it is free to rotate about one of its edges. Now, the rod rotates with an angular acceleration α under the influence of a force F applied on the other end. We can find out α easily with the torque equation (Given that mass & length of rod is m & L). Now in this condition, if we apply torque equation on the COM of the rod, the angular acceleration that we have here is same. enter image description here

Note: $F_1$ & $F_2$ are the forces provided by the hinges.


2) Now almost the same case, the only difference is that now, the force ‘F’ is acting on the COM, and we’ve to find angular acceleration of the rod about a)hinges b)the other end. Case 2

Why is the angular acceleration different? Doesn’t it has to be the same?

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closed as off-topic by Emilio Pisanty, Kyle Kanos, Jon Custer, stafusa, ZeroTheHero Jul 8 '18 at 2:59

This question appears to be off-topic. The users who voted to close gave this specific reason:

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    $\begingroup$ Hi, welcome to Physics SE! Please don't post formulae as pictures, but use MathJax instead. MathJax is easy for people on all devices to read, and can show up clearer on different screen sizes and resolutions. $\endgroup$ – user191954 Jul 5 '18 at 6:02
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    $\begingroup$ Also, please note that check-my-work questions are generally considered off-topic here. We intend our questions to be potentially useful to a broader set of users than just the one asking, and prefer conceptual questions. Can you try making a question about some concepts that you'd need to solve this problem? $\endgroup$ – user191954 Jul 5 '18 at 6:24
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The hinge is not accelerating. So when considering torques about that axis, the analysis is simple.

The center of mass is accelerating. So when looking at torques about that axis, it is at rest in a non-inertial reference frame. Fictitious forces will appear in that frame. But since the forces that appear act through the center of mass, they apply no torque. So the analysis is again simple.

Point A is also accelerating. So when looking at the torque about it, you have to consider the fictitious forces that appear due to the acceleration of the axis.

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