Static 9 and 10

CE 2010 Handout #9 Section 4.5 (Exam #2)

Learning Objectives

 Determine the moment of a force about an axis.

Moment of a Force About an Axis – Scalar Analysis

 MO = Fd where F and d are perpendicular.

 Direction of MO is found using the ________________________.

 Components of MO are parallel to the x, y and z axes.

 _____________ can be used to find components parallel and perpendicular to other axes.

 If F is perpendicular to any axis aa, Ma = Fda, where da is the perpendicular distance between a and

F.

 If F or one of its components is parallel to an axis, it cannot cause a moment about that axis.

 If a force’s line of action passes through an axis, it cannot cause a moment about that axis.

Moment of a Force About an Axis –Vector Analysis

 most common approach

 Review: The _________ ________________ is used to find components of a vector that projects

onto another axis, i.e., is parallel to another axis.

 When it’s desired to find the component of a moment parallel to an axis, the ________

__________________ is also used.

 M = r x F. The dot product for M parallel to a unit vector along axis a,

Ma = ua∙ (r x F) =

 Since only i ∙ i = 1, j ∙ j = 1 and k ∙ k = 1, the components of ua can be included in the matrix

calculation:

 This is called the _________________ _____________________ _________________.

CE 2010 Handout #9 Section 4.5 (Exam #2)

Ex #1 Determine the moment of the force F about the OA

axis. Express the result as a Cartesian vector.

Ex #2 Determine the magnitude of the moment of the

force F = [50i – 20j – 80k] N about the base line CA of the

tripod.