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I am having a hard time taking care of signs. Whether we’ve made the cut at right or at left. Whether should we make the rotation according to axis x, y or z. In this case, they assumed that P was applied at the left of the axis of rotation and obtained M as negative. Why couldn’t we assumed that P is at right as well and with the calculations shown be positive?

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Both moments tend to turn the plate in the same direction (counter-clockwise). So both should have the same sign. If you use convention used in the book, then both are negative: https://classes.mst.edu/civeng2210/concepts/07/internal/index.html

However, if you use the screw rule both are positive: http://www2.eng.cam.ac.uk/~hemh1/gyroscopes/screwrule.html

So both must have the same sign and the result is then the same.

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  • $\begingroup$ in the figure at left,M is shown to be counterclockwise to positive according to our conventions. However, in the formula at right they used M as negative $\endgroup$ – Roy Rizk May 8 '19 at 19:06
  • $\begingroup$ And assuming the force was at the right of the axis it should’ve been positive and opposite to the counterclockwise direction of the one shown at the cut $\endgroup$ – Roy Rizk May 8 '19 at 19:08
  • $\begingroup$ True. Then the moment and the moment created by the force should have opposite signs. $\endgroup$ – user20096 May 8 '19 at 20:32

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