tailieunhanh - Introduction to Statics and Dynamics Part 2

Vector notation and vector addition Graphical: a scalar multiplies an arrow. Indicate a vector’s direction by drawing an arrow with direction indicated by marked angles or slopes. The scalar multiple with a nearby scalar symbol, say F, as shown in figure . This means F times a unit vector in the direction of the arrow. (Because F might be negative, sign confusion is common amongst beginners. Please see sample .) Combined: graphical representation used to define a symbolic vector. The full symbolic notation can be used in a picture with the graphical information as a way of defining the symbol | . Vector notation and vector addition 13 Graphical a scalar multiplies an arrow. Indicate a vector s direction by drawing an arrow with direction indicated by marked angles or slopes. The scalar multiple with a nearby scalar symbol say F as shown in figure . This means F times a unit vector in the direction of the arrow. Because F might be negative sign confusion is commonamongst beginners. Please see sample . Combined graphical representation used to define a symbolic vector. The full symbolic notation can be used in a picture with the graphical information as a way of defining the symbol. For example if the arrow in fig. were labeled with an F instead of just F we would be showing that F is a scalar multiplied by a unit vector in the direction shown. The components of a vector A given vector say F canbe described as the sum of vectors each of which is parallel to a coordinate axis. Thus F Fx Fy in 2D and F Fx Fy Fz in 3D. Each of these vectors can in turn be written as the product of a scalar and a unit vector along the positive axes . Fx Fxi see fig. . So F Fx Fy Fx i Fy j 2D or F Fx Fy Fz Fx i Fy j Fz k. 3D The scalars Fx Fy and Fz are called the components of the vector with respect to the axes xyz. The components may also be thought of as the orthogonal projections the shadows of the vector onto the coordinate axes. Because the list of components is such a handy way to describe a vector we have a special notation for it. The bracketed expression F xyz stands for the list of components of F presented as a horizontal or vertical array depending on context as shown below. f xyz Fx Fz or F xyz Fx Fy Fz Fy If we had an xy coordinate system with x pointing East and y pointing North we could write the components of a 5N force pointed Northeast as F xy 5 V2 N 5 V2 N . Note that the components of a vector in some crooked coordinate system x y z are different than the coordinates for the same vector in the coordinate system xyz because the .