 | Sidney Luxton Loney - Dynamics - 1891 - 318 pages
...algebraic sum of the resolved parts of all the forces in a perpendicular direction. III. Equate to zero the algebraic sum of the moments of the forces about any point in their plane. The above three statical relations, together with the geometrical relations holding between the component... | |
 | Leander Miller Hoskins - Graphic statics - 1892 - 236 pages
...(not shown) its magnitude. By the principle of moments (Art. 50) the sum of the moments of AB and BC about any point in their plane is equal to the moment of AC about the same point. If the origin of moments is on ac, the moment of AC is zero ; and therefore... | |
 | Alexander Ziwet - Mechanics, Analytic - 1893 - 216 pages
...can now be stated in the following form : the algebraic sum of the moments of any tivo intersecting forces about any point in their plane is equal to...the moment of their resultant about the same point. 92. The product Rr represents twice the area of the triangle having R for its base and 5 for its vertex... | |
 | Augustus Jay Du Bois - Mechanics, Analytic - 1894 - 420 pages
...Q, we have AD cos a, = p, CD cos a = r, BD cos a, = q, and hence 4- Pp - Rr - Qq = 0. That is, the algebraic sum of the moments of the forces about any point in their plane is zero (page 99). Again, suppose the lever to be translated in any direction through an indefinitely... | |
 | William Briggs, George Hartley Bryan - Statics - 1894 - 254 pages
...2. — When any number of coplanar forces* act on a rigid body, the algebraic sum of their moments about any point in their plane is equal to the moment of their resultant. Consider two of the forces. Whether these intersect or are parallel, algebraic sum of their moments... | |
 | Augustus Jay Du Bois - Mechanics, Analytic - 1894 - 424 pages
...negative (— ). Also angles with OX and OF are measured from OJTand OF around towards the left. 2d. The algebraic sum of the moments of the forces about any point in their plane must be zero. Hence if p, , pt , p> , etc., are the perpendiculars from any given point in the plane... | |
 | Augustus Jay Du Bois - Mechanics, Analytic - 1894 - 414 pages
...the forces in each of any two rectangular directions in the plane of the forces must be zero. 2d. The algebraic sum of the moments of the forces about any point in this plane must be zero. If the first condition only is satisfied, we have molar equilibrium. If the... | |
 | Sir Richard Glazebrook - Hydrostatics - 1896 - 204 pages
...great importance. PROPOSITION 15. To prove that the algebraic sum of the moments of two forces about a point in their plane is equal to the moment of their resultant about that point. (i) When the lines of action of t/te forces meet. Let the forces be P, Q impressed on a... | |
 | Thomas Wallace Wright - Mechanics - 1896 - 418 pages
...twice the area of the triangle. 5. Show that the sum of the moments of the two forces forming a couple about any point in their plane is equal to the moment of the couple. 139. General Method of Combining Forces (Analytical). — It is evident from the preceding... | |
 | Sir Philip Magnus (bart.) - Mechanics - 1896 - 408 pages
...forces in directions at right angles to each other, we must have JT=0 and F=?0. And RX AB equals the algebraic sum of the moments of the forces about any point in the same plane. Hence, we have as the general conditions of equilibrium, (1) JT, + Z, + X3 + . . .... | |
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Prove that the algebraic sum of the moments of two concurrent forces about any point in their plane is equal to the moment of their resultant about the same point. 
