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(a) A force has zero moment about any point along its line of action. (b) A force has no moment about a line parallel to its line of action. (c) The magnitude of the moment of a force about a line equals the product of the component of the force perpendicular to the line and the distance between this component and the line.

(a) A force has zero moment about any point along its line of action. (b) A force has no moment about a line parallel to its line of action. (c) The magnitude of the moment of a force about a line equals the product of the component of the force perpendicular to the line and the distance between this component and the line.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Answer true or false in response to the following questions:** (a) A force has zero moment about any point along its line of action. (b) A force has no moment about a line parallel to its line of action. (c) The magnitude of the moment of a force about a line equals the product of the component of the force perpendicular to the line and the distance between this component and the line. (d) The moment about a point P of the sum of a set of concurrent forces, placed at the point of concurrency (point P), equals the sum of the moments about P of the separate forces. (e) A couple has the same moment about any point. (f) If we know the moment of a couple about a point A, then we can find the moment of the couple about a specified line BC even if A does not lie on BC. (g) Two force and couple systems are equipollent if they have either the same resultant force or if the moments about some point P are the same for both systems. (h) It is possible for a system consisting of a single couple to be equipollent to a system of one force and 99 couples. (i) Given any system of forces and couples, and any point P, the system may be reduced to an equipollent system comprising of a force at P and a couple (where either or both might be zero). (j) If a system \( S_1 \) of forces and couples has a “force-alone” (single force resultant) equipollent system \( S_2 \), then \( S_1 \) must be a coplanar force system. (k) The simplest resultant of a general system of forces and couples is a “wrench” or “screwdriver,” that is, a collinear force and a couple along a specific axis in space. (l) Let a general system of forces and couples be resolved into a resultant force at P and an accompanying couple. If the couple is normal to the force, then the equipollent wrench consists of a single force. (m) If a body is in equilibrium under the action of three forces, and two of these intersect at a point P, then the line of action of the third also passes through P. (n) If a body is in equilibrium under four forces, two of which form a couple, then the other two also form a couple. (o) If a body is in equilibrium under the action of three forces, the
Transcribed Image Text:**Answer true or false in response to the following questions:** (a) A force has zero moment about any point along its line of action. (b) A force has no moment about a line parallel to its line of action. (c) The magnitude of the moment of a force about a line equals the product of the component of the force perpendicular to the line and the distance between this component and the line. (d) The moment about a point P of the sum of a set of concurrent forces, placed at the point of concurrency (point P), equals the sum of the moments about P of the separate forces. (e) A couple has the same moment about any point. (f) If we know the moment of a couple about a point A, then we can find the moment of the couple about a specified line BC even if A does not lie on BC. (g) Two force and couple systems are equipollent if they have either the same resultant force or if the moments about some point P are the same for both systems. (h) It is possible for a system consisting of a single couple to be equipollent to a system of one force and 99 couples. (i) Given any system of forces and couples, and any point P, the system may be reduced to an equipollent system comprising of a force at P and a couple (where either or both might be zero). (j) If a system \( S_1 \) of forces and couples has a “force-alone” (single force resultant) equipollent system \( S_2 \), then \( S_1 \) must be a coplanar force system. (k) The simplest resultant of a general system of forces and couples is a “wrench” or “screwdriver,” that is, a collinear force and a couple along a specific axis in space. (l) Let a general system of forces and couples be resolved into a resultant force at P and an accompanying couple. If the couple is normal to the force, then the equipollent wrench consists of a single force. (m) If a body is in equilibrium under the action of three forces, and two of these intersect at a point P, then the line of action of the third also passes through P. (n) If a body is in equilibrium under four forces, two of which form a couple, then the other two also form a couple. (o) If a body is in equilibrium under the action of three forces, the
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