Lecture 2: Vectors and Force Systems

• Is any positive or negative physical quantity that can be completely classified by its magnitude

  scalar
• is any physical quantity that requires both a magnitude and direction for its complete description

  vectors
• whose action is not confined to or associated with a unique line in space

  free vector
• has a unique line of action in space but not a unique point of application

  sliding vector
• for which a unique point of application is specified

  fixed vector
• is the process of determining the resultant of vectors

  composition of vectors
• the characteristics of a force:

  • magnitude
  • direction
  • point of application
  • line of action
• is produced by direct physical contact

  contact force
• generated by virtue of the position of a body within a force field such as gravitational, electric or magnetic field

  body forces
• force that is considered to act on a point

  point load or concentrated load
• applied across a length or area instead of a one point

  distributed load
• forces that originate within an object

  internal forces
• forces that act on an object or system from outside

  external forces
• two main subsections of force system:

  • coplanar
  • non coplanar
• forces under coplanar:

  • collinear
  • parallel
  • concurrent
  • non concurrent
• forces under non coplanar:

  • parallel
  • concurrent
  • non concurrent
• when the lines of action of all forces of a system act along the same line

  collinear force system
• forces that are parallel from one another

  parallel forces
• when the lines of action of all the forces lie in a single plane

  coplanar force system
• when the line of action of all the forces does not lie on a single plane

  non coplanar force system
• when the forces of a system do not meet at a common point of concurrency

  non concurrent force system
• unit vector is also known as

  direction vector
• it is defined as the cosines of the angles between the three coordinate axes and the vector

  directional cosines
• r is defined as a fixed vector that locates a point in space relative to another point

  position vector
• the process is done by the algebraic addition or subtraction of all similar vector components at their respective axes


  vector addition and subtraction
• vector dot product produces a

  scalar quantity
• applications of dot product:

  • find the angle of two vectors
  • find the orthogonal projection and perpendicular line
• cross product yields a

  vector quantity
• properties of vector cross product:

  • Non commutative
  • multiplicative by scalar
  • distributive
• when the cross product of two vectors is dotted with a third vector

  scalar triple product