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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr.mun.ca 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 http://www.engr.mun.ca/~societya/ http://www.socb.ca/sample_finals.html

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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 18-01 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 18-02 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) http://wps.prenhall.com/esm_hibbeler_eng mech_1

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Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI.

Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI.

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