Example 4.2.1. Sign Conventions.
For each scalar component, determine whether the moment is clockwise or counterclockwise, and apply the right-hand rule to determine the direction of the corresponding moment vector.
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\(\displaystyle M_1 = \Nm{30}\)
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\(\displaystyle M_2 = \kNm{-400}\)
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\(\displaystyle M_3 = \Nm{25} \circlearrowright\)
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\(\displaystyle M_4 = \ftlb{-100} \circlearrowright\)
Solution.
By the right-hand rule, counterclockwise moments in the \(x\)-\(y\) plane are vectors that point in the \(+\khat\) direction. The corresponding scalar component has a positive sign. Clockwise moments point in the \(-\khat\) direction and have a negative sign.
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The arrow on \(M_3\) establishes the positive direction as CW. A positive scalar component means that the direction is CW and the vector points in the \(-\khat\) direction.
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The arrow on \(M_4\) establishes the positive direction as CW, but the negative sign on the scalar component means that the actual moment is CCW. The vector points in the \(+\khat\) direction.