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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI 1313 Mechanics I Lecture 18:Moment of a Force About a Specified Axis

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 2 Mid-Term For This Class Date:October 18 Time: 830am-945am Location: to be determined Material:Up to and including problem set #4 Alternate Exam Onlyand Only if there is a compelling reason to miss October 18 th and I must be informed by October 15 th with reason provided Date:October 22 Time: 700pm-815pm Location: EN 2007 Material:Up to and including problem set #4

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 3 Mid-Term (cont.) General Comments All students will be required to take the examination Resources Tutorial problem sets Quiz problems Student societies

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 4 Lecture 18 Objective to provide scalar and vector methods for determining the moment of a force about a specified axis

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 5 Moment About a Specified Axis The axis of the moment (Mo) about point O is perpendicular to force (F) and position vector (r) plane What is the component moment about the x-, y- or z-axes? Why is this information important? MxMx MyMy MzMz

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 6 Moment About a Specified Axis (cont.) What is the Moment About Point O?

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 7 Moment About a Specified Axis (cont.) What is the Moment About the X-Axis? Tending to bend the pipe about O MxMx

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 8 Moment About a Specified Axis (cont.) What is the Moment About the Y-Axis? Tending to unscrew the pipe about O MyMy

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 9 Moment About a Specified Axis (cont.) L

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 10 Moment About a Specified Axis (cont.) Moment Vector About Point O Use cross product

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 11 Moment About a Specified Axis (cont.) Moment Vector About Point O

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 12 Moment About a Specified Axis (cont.) Moment Component Projected on Y-axis Recall dot product

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 13 Triple Scalar Product Generalized Statement Determine the component moment magnitude (|M a |) on a specified axis due to the moment (M o )

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 14 Triple Scalar Product (cont.) Determine the component moment magnitude (|M a |) on a specified axis due to the moment (M o )

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 15 Triple Scalar Product (cont.)

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 16 Triple Scalar Product (cont.)

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 17 Triple Scalar Product (cont.)

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 18 Triple Scalar Product (cont.)

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 19 Moment Vector on Specified Axis Determine the moment vector (M a ) on a specified axis due to the moment (M o ) r r

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 20 Comprehension Quiz The force F is acting along DC. Using the triple product to determine the moment of F about the bar BA, you could use any of the following position vectors except ______. A) r BC A) r AD C) r AC D) r DB A) r BD Answer: D Force Line of Action Moment Axis

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 21 Comprehension Quiz For finding the moment of the force F about the x-axis, the position vector (r) in the triple scalar product should be ___. A) r AC A) r BA C) r AB D) r BC Answer: C

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ENGI 1313 Statics I – Lecture 18© 2007 S. Kenny, Ph.D., P.Eng. 22 References Hibbeler (2007) mech_1

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