mechanika

• Two force systems are equivalent if their total moments about two points are equal and

  projections of their sums on the line connecting these points are equaL
• WHAT DOES IT MEAN TO determine the simplest equivalent force system to a given system?

  • to find a system of forces we can replace it with thats simpler but equivalent
  • To reduce a system of forces means to replace it with the equivalent, simpler system
• moment of a force ,,F'' APPLIED AT POINT ,,A'' about point B

  is equal to the cross product of the force vector and the vector AB

  • line of action of the MOMENT is PERPENDICLUAR TO TO both F and AB
• moment of a force about a line

  is equal to the projection of the force onto a plane perpendicular to this line

  -about point of intersection of this plane and line

  • moment of a force about a line is PARALLEL to this line
• system decribed by

  • sum vector
  • moment about a point

  INVARIANTS

  • K -parameter
  • sum vector
• moment transport theorem

  1. If the sum of any given force system equals zero then the total moment of this system is constant S=0 --> M=const.
  2. f the moments of a force system about THREE non-collinear points are equal, then the sum of this system equals ZERO
  3. For an arbitrary force system the dot product of its sum and its moment about any point is constant and called THE PARAMETER OF THE SYSTEM
• PLANAR

  all forces act in one plane

  -k=0

  • The sum vector is parallel to the plane
• PARALLEL

  forces act along parallel lines

  -parallel lines of action

  • k=0
• CONCURRENT

  THE LINES OF ACTION of all forces INTERSECT at one point

  M=0 --> k=0
• central axis 


  line cointaing centres of reduction about which moment is minimal
• centre of parallel force system property

  new system from ratation all forces around their points of application by the same angle

  • central axes of both systems intersect in the CENTRE OF PARALLEL FORCE SYSTEM
• Reduction of aforce system about a chosen point

  reduced to one force and one couple

  • force equal to SUM VECTOR
  • couple equal to the total moment of a system
• To reduce the force system to the simplest equivalent system means

  to find the equivalent system comprising the smallest number of forces.
• The principal axes of inertia of a rigid body are a set of axes passing through the object's center of mass