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Hi, friends!!! I'm having some trouble understanding the constraint equations:-

(1) How do they relate the length of the string to the position of the block attached to it? The position of the block must be a vector and it must be differentiated to get the velocity and then the acceleration. However in my book, they have just differentiated the length of the string, which they have taken as the position of the block, to get the velocity and then the acceleration.....

(2) Are they scalar or vector relations???

(3) Are the with always derived with respect to some fixed frame of reference???

(4) If no in question (3), do we consider relative velocities/accelerations in moving pulleys, like acceleration of block with respect to pulley, and then use the relative velocity/acceleration equation????

(6) Are they applicable to all kinds of pulley-string-block arrangements, because I was under the impression that it is applicable only if the blocks move in opposite directions....

(7) Are constraint equations coordinate system and origin (fixed) dependent, or are they general relations applicable in all (fixed) coordinate systems???

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# How do constraint equations in mechanics work?

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