U6 Mechanics

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

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 .