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Can we take rotational equilibrium of only one part of a body? Such as in a step ladder, where BD is a rope.

Can we take rotational equilibrium of AC about C, and not the full ladder? Step Ladder

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Of course. The conditions for equilibrium can be applied to any part of an object in equilibrium. Not only to the obvious structural divisions into parts such as the legs AC, CE and the horizontal step at C and the link BD, but also to any abstract division such as an irregular-shaped chunk of one leg. You consider that part to be isolated from the rest of the universe, draw a free body diagram for it, and consider the effect of the forces acting on it.

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Yes you can. Free body diagrams always helps to isolate a system from the surrounding. It helps us to eliminate those forces whose information is unknown. How?? In your case the rope obviously pulls the ladder with some tension. But if we consider the whole structure as the system the tension in the rope gets cancelled out (both action and reaction pairs being inside the system).

Coming to your question, it has been said that the whole structure is in rotational equilibrium which implies that each and every part of the system is in equilibrium. So you can choose your FBD accordingly. In your case taking half of the ladder and half of the rope would answer your question.

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