Physics for Engineers: Vectors (PDF)

 CONCEPTS AND PRINCIPLES FORCE The action exerted by one body upon another. Force may be defined as any action that tends to change the state of rest or motion of a body to which it is applied. CHARACTERISTICS OF A FORCE : 1. MAGNITUDE The quantitative effect of a force....

 CONCEPTS AND PRINCIPLES FORCE The action exerted by one body upon another. Force may be defined as any action that tends to change the state of rest or motion of a body to which it is applied. CHARACTERISTICS OF A FORCE : 1. MAGNITUDE The quantitative effect of a force. 2. POINT OF APPLICATION the exact location at which a force is applied to a body. 3. DIRECTION Direction of application is where the force moves along the line of action FORCE SYSTEM: CONCURRENT FORCES are forces whose lines of action are passing through one common point. NON-CONCURRENT FORCES When the forces of a system do not meet at a common point of concurrency. COLLINEAR FORCES When the lines of action of all the forces of a system act along the same line PARALLEL FORCE are forces in the same direction whose lines of action never meet.  COPLANAR FORCE When the lines of action of a set of forces lie in a single plane is called coplanar force system. NON-COPLANAR FORCE When the line of action of all the forces do not lie in one plane, is called Non-coplanar force system SCALAR QUANTITY quantities completely specified by a single value with an appropriate unit and has no direction. VECTOR QUANTITY quantities that have both numerical and directional properties. VECTORS represent physical quantities which have magnitude and a direction. Vectors are identified by a symbolic name which will be typeset in bold like F to indicate its vector nature. Examples: displacement, velocity, weight, moment and acceleration COMPONENT OF A VECTOR A component is a projection of a vector along an axis. The x-component of a vector is 𝑨𝒙 = 𝑨 cos 𝜽 the projection along the x-axis. The y-component of a vector is 𝑨𝒚 = 𝑨 sin 𝜽 the projection along the y-axis. With the components known, the 𝟐 𝟐 magnitude of the vector is given 𝑨 = 𝑨𝒙 + 𝑨𝒚 by: The angle of the vector with the 𝑨𝒚 x-axis can be found from the tan 𝜃 = 𝑨𝒙 relation: VECTORS MAGNITUDE Positive real number including units which describes the intensity or strength of the vector. UNIT VECTORS A unit vector is a vector that has a magnitude of 1, with no units. Its only purpose is to describe a direction in space. Components of vectors can be expressed using unit vector notations, x-comp is 𝑖 and y-comp is 𝑗. Example: 2 Dimension 3 Dimension 𝑦 𝑧 (𝒂𝟏 , 𝒂𝟐 ) (𝒂𝟏 , 𝒂𝟐 , 𝒂𝟑 ) 𝑨 = 𝑎1 , 𝑎2 ෙ 𝑥 𝒌 𝑦 𝒊Ƽ 𝒋 𝑨 = 𝑎1 , 𝑎2 , 𝑎3 𝑥 Can be written in the form: 𝒙𝑖Ƽ + 𝒚𝑗+ 𝒛𝑘ෘ or (𝑥, 𝑦, 𝑧)  VECTOR OPERATIONS VECTOR ADDITION Vectors can be added according to Parallelogram Law or Triangle Rule. If more than two vectors are to be added, the same may be done first by adding the two vectors, and then by adding the third vector to the resultant of the first two and so on. This method of adding more than two vectors is called Polygon Law of Addition of Vectors. 𝑨+𝑩=𝑹 VECTOR SUBTRACTION means the addition of negative vectors. The vector subtraction of two vectors a and b is represented by 𝑨 - 𝑩 and it is nothing but adding the negative of vector b to the vector a. i.e., 𝑨 - 𝑩 = 𝑨 +(-𝑩). Thus, subtraction of vectors involves the addition of vectors and the negative of a vector. 𝑨-𝑩=𝑹 𝑨 +(-𝑩) = 𝑹  WHEN RESULTANT SENDING A MESSAGE FORCE the resultant force describes the net force acting on the object. The value of resultant determines the motion of the object. Forces CORRECT acting at some angle from the coordinate WRONG axes can be resolved into mutually perpendicular forces called components. Good morning, Ma’am! My Hi behhh