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Stability
Published in Rose G. Davies, Aerodynamics Principles for Air Transport Pilots, 2020
The magnitude and direction of a moment m produced by a force depend on the magnitude of the force and the relative position of the force to the pivot point, or the rotating center. As shown in Figure 5.2 (a), a force F acts on one end of a stick vertically; the length of the stick is l, and the pivot is “O” at the other end of the stick. d is the (perpendicular) distance between the force and the pivot point. The angle between l and d is α. The moment caused by F about “O” is: M=Fd=Flcosα
Control of Movement and Posture
Published in Nassir H. Sabah, Neuromuscular Fundamentals, 2020
where the right-hand side and left-hand side represent the moments of F and L, respectively, about the fulcrum. cosθ cancels out from both sides of Equation 13.1. The moment of a force about a point of rotation can be interpreted as: (i) the product of the magnitude of the force and the perpendicular distance from the point of rotation to the line of action of the force, or (ii) the product of the distance from the point of application of the force to the point of rotation, along the length of the rigid member, and the magnitude of the component of the force perpendicular to the rigid member.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
where d is the moment arm or perpendicular distance from the point to the line of action of the force, as in Figure 1.4. The direction of the moment is defined by the right-hand rule, whereby the curl of the right-hand fingers follows the tendency for rotation caused by the force, and the thumb specifies the directional sense of the moment. In this case, MO is directed out of the page, since F produces counterclockwise rotation about O. It should be noted that the force can act at any point along its line of action and still produce the same moment about O.
Geotechnical analysis of blasting sequence and resulting shapes of drawbells in block cave mines
Published in Mining Technology, 2023
Nadia Bustos, Ernesto Villaescusa, Italo Onederra
In this work, the dynamic burden is calculated as a horizontal distance from a drilled hole to a defined free face by a relative level (R.L.) starting upwards from the drawpoint roof. Each of the drilled holes was numbered according to its designed timing sequence. A Bn (n = hole number according to the timing) was calculated as the minimal distance between calculations a, b and c: The perpendicular distance between each hole to the closest border of the up-hole raise (see Figure 4(a)).The closest perpendicular distance to a line connecting two previously detonated holes. Figure 4b1 shows an example in detail for the calculation for hole 5. A scheme with a progressing result for holes 1–11 is shown in Figure 4(b2).Distance between all the holes: In some particular locations, the distance between the line formed for two holes previously blasted is larger than the direct distance between 2 holes. An example of it occurs in Hole 14 shown in Figure 4(c).
Uniqueness of billiard coding in polygons
Published in Dynamical Systems, 2021
In the case where , there is a hole in lying between and or lying between and . As illustrated by Figure 13(a), since the minimal diameter of the hole is strictly greater than δ, there exists some point in whose distance to is greater than δ, which is in turn greater than by (). Thus, the perpendicular distance from some point in to must be greater than .
Enhanced model including moment-rotation dependency for stability of thin-walled structures
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2020
Atef S. Gendy, Samir S. Marzouk
Using the above equations (i.e., Eqs. (6) and (10)), one can arrive at the “resultant-type” constitutive expression; i.e., where the symmetric (8 × 8) matrix C is the spatial elasticity tensor, i.e., section-rigidities (or moduli) matrix; i.e., where Diag. [ ] denotes a diagonal matrix. In addition to the well-known axial, shear and bending stiffness coefficients in the first five diagonal terms in Eq. (12) (Asi = α Ai, for i = y, z are the flexural shear correction factors [1, 3, 5]), the following St. Venant and warping torsion rigidities are defined as [4], [22], and [23] where ρ is the perpendicular distance from the shear center to the tangent to the sectorial profile at considered point [3].