# Lecture 10 - ENGR-1100 Introduction to Engineering Analysis...

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Lecture 10 Notes courtesy of: Prof. Yoav Peles ENGR-1100 Introduction to Engineering Analysis

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Homework Assignment (due next class) Problem 4-54 Problem 4-59 Problem 4-64
Lecture Outline Vector representation of a moment: - Moment of a force about a point. -Moment of a force about a line.

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F d Ο In 2D, we work in the plane perpendicular to the axis that contains F . Point O is intersection of axis A-A with that plane. The magnitude of the moment is: M = | F |d where: F = force; and d = perpendicular distance from the line of action of the force to the axis (point O). Units of Moment M : lb•ft or lb•in in U.S. Customary system ; and N•m or kN•m in SI units.
F d Ο α 1 Α 1 α 2 Α 2 r 1 r 2 sin α 1 = d / r 1 sin α 2 = d / r 2 d = r 1 sin α 1 = r 2 sin α 2

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Two dimensional case F = F x i + F y j r = r x i + r y j x y r F O A j i M 0 = r x F = (r x i + r y j ) x (F x i + F y j ) = r x F x ( i x i ) + r x F y ( i x j ) + r y F x ( j x i ) + r y F y ( j x j ) = (r x F y - r y F x ) k = M z k M 0 = = (r x F y - r y F x ) k = M z k i j k r x r y 0 x y
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Lecture 10 - ENGR-1100 Introduction to Engineering Analysis...

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