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In physics, the line of action (also called line of application) of a force (F →) is a geometric representation of how the force is applied. It is the straight line through the point at which the force is applied, and is in the same direction as the vector F →. [1] [2] The concept is essential, for instance, for understanding the net effect ...
Suppose a particle moves at a uniform rate along a line from A to B (Figure 2) in a given time (say, one second), while in the same time, the line AB moves uniformly from its position at AB to a position at DC, remaining parallel to its original orientation throughout. Accounting for both motions, the particle traces the line AC.
The component of the force parallel to the motion, or equivalently, perpendicular to the line connecting the point of application to the axis is . The sum is over j {\displaystyle j} from 1 {\displaystyle 1} to N {\displaystyle N} particles and/or points of application.
A single force acting at any point O′ of a rigid body can be replaced by an equal and parallel force F acting at any given point O and a couple with forces parallel to F whose moment is M = Fd, d being the separation of O and O′. Conversely, a couple and a force in the plane of the couple can be replaced by a single force, appropriately ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
If F is a central force, it must be parallel to the vector r B from the center O to the point B (dashed green line); in that case, Δr is also parallel to r B. If no force acts at point B , the velocity is unchanged, and the particle arrives at point K at time t = 2Δ t .
When two forces act on a point particle, the resulting force, the resultant (also called the net force), can be determined by following the parallelogram rule of vector addition: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that is equal in magnitude and direction to the transversal ...
Thus, the vector is parallel to , the vector is orthogonal to , and = +. The projection of a onto b can be decomposed into a direction and a scalar magnitude by writing it as a 1 = a 1 b ^ {\displaystyle \mathbf {a} _{1}=a_{1}\mathbf {\hat {b}} } where a 1 {\displaystyle a_{1}} is a scalar, called the scalar projection of a onto b , and b̂ is ...