Kinematics


   
 
Resolution and Components of Vectors in a Plane
The process of splitting a vector is called resolution of a vector. In simpler language it would mean, determining the effect of a vector in a particular direction. This is explained with the help of an example later on. The parts of the vector obtained after splitting the vector are known as the components of the vector.
 
 
 
Applying the law of triangle of vectors,
 
 
 
 
Rectangular components of a vector
If the components of a given vector are perpendicular to each other, they are called rectangular components. The figure illustrates a vector represented by . Through the point, O two mutually perpendicular axes X and Y are drawn. From the point P, two perpendiculars, PN and PM are dropped on X and Y axes respectively.
 
 
 
 
of A.
 
Moreover, in the right-angled DONP, Cosq = Ax / A or Ax = A Cosq --(1)
 
 
 
 
Squaring and adding 1 and 2,
 
 
 
 
 
This equation gives the magnitude of the given vector in terms of the magnitudes of the components of the given vector.
 
 
where
 
 
Example of resolution of vector
An example of resolution of a vector is the way a person walks. When a person walks, he/she presses the ground obliquely, (i.e., at an angle to the ground) in the backward direction. The ground offers an equal and opposite reaction in the opposite direction. The vertical component of this reaction balances the weight of the person. The horizontal component helps the person to walk.
 
  
     
   
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Kinematics

  		•  Uniform Motion - Introduction
  		• Concept of a Point Object
  		• Rest and Motion
  		• Motion in One, Two and Three Dimensions
  		• Motion in a Straight Line
  		• Position-Time Graph for Non-Uniform Motion
  		• Graphical Representation of Uniform Motion
  		• Uniformly Accelerated Motion - Introduction
  		• Uniformly Accelerated Motion - Introduction
  		• Velocity-Time Graphs of Accelerated Motion
  		• Relations for Uniformly Accelerated Motion (Graphical Treatment)
  		• Position-Time Relations using Position-Time Graphs
  		• Distance as Area under Velocity-Time Graph
  		• Velocity-Time Relations using Calculus
  		• Velocity-Distance Relation
  		• Vectors - Introduction
  		• Definitions
  		• Unit Vector
  		• Fixed Vector
  		• Displacement Vector
  		• Multiplication of Vectors by Real Numbers, i.e., Scalar Multiple of a Vector
  		• Equality of Vectors
  		• The Zero Vector and its Properties
  		• Addition or Composition of Vectors
  		• Parallelogram Law of Vectors
  		• Law of Polygon of Vectors
  		• Resolution and Components of Vectors in a Plane
  		• Dot Product of Vectors and the Resolution of a Vector
  		• Relative Velocity in the Case of Two Velocities Inclined to Each Other
  		• Cross Product or Vector Product of Two Vectors
  		• Motion in a Plane - Introduction
  		• Case of Uniform Velocity
  		• Case of Uniform Acceleration
  		• Expression for Velocity Vector
  		• Projectile Motion
  		• Oblique Projectile
  		• Maximum Height
  		• Uniform Circular Motion
  		• Summary
    Animations
  		• Motion
  		• Difference between Distance and Displacement
  		• S - t Graph or Distance - Time Graph
  		• v - t Graph or Velocity - Time Graph
  		• Speed - Time Graph
  		• Scalar Product and Vector Product of two Vectors
  		• Projectile Motion