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Notes on systems of parallel forces

With systems of forces acting on a particle, it follows that all the forces have a line of action passing through the same point, which is the particle. In such cases, if the system is not in equilibrium, we can find a single resultant force which also acts through the same point and we can state the magnitude and direction of this resultant. There is no turning effect because all the forces, including the resultant, have zero perpendicular distance of their line of action from the object being considered, (the particle). If we have a system of forces which do not all pass through the same point, then if the system is not in equilibrium, we must find a resultant force and specify its magnitude and direction as before, but we must also state where its line of action is positioned. There are now many different possible arrangements of forces, so let's simplify by considering some of the general possibilities. First let's consider the type of situation where all the forces are

Ex7A Qu28

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An example to introduce the Principle of Moments

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This example will show how useful the Principle of Moments will be. I will first calculate the moment of a force in a rather difficult direction and then I will show how this could have been calculated in a much simpler way. EXAMPLE: Calculate the moment about the origin of a force F = -4 i + j , which is acting through the point r = 5 i + 2 j .

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Ex7A Qu 13

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Ex7A Qu 1

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Note that turning effect or moment or torque can all be taken to mean the same thing.

Week 1: March 30th 2020

[I am going to start by assuming that you have a copy of "Understanding Mechanics" by Sadler and Thorning. If you haven't, then please send me a message. I am also providing some other resources as we go along. First extra resource is Chapter 9 section 1 of "A complete A-level Maths" by Gough. You will find this indicated by "Gough 9.1" in the Resources menu.] Our first topic in this series is "Moments". Please read Chapter 7 Moments in Sadler and Thorning, from page 134 to p137 and then I will post some worked examples.

Welcome

Welcome to the blog for Upper Sixth Form Mechanical Mathematics! I will try to post something at least once a week.