Tuesday, April 23, 2013

Vector Diagrams & Analysis

Vector Diagrams & Analysis

An Introduction to visualizing force, frictions, acceleration, and displacement

Through out our study of the Human Body and the many directions we are capable of moving, we will us vector analysis to visualize the Physical aspects of every type of movement.  Before you are able to diagram the physics of any situation, you must be able to differentiate between scalar and vector quantities. Note that in science, we use the International System of units, abbreviated SI Units, i.e. meter not yards, kilograms not pounds, etc. 


In Newtonian Physics, A physical quantity that is not changed by coordination system rotations or reflections is known as a scalar.  (The Coordinate system is best represented by the unit circle pictured above in the Mathematical Movement banner.) Basically scalars have no directions; however, it is more than a number because physical quantities are an expression of numerical value and a physical unit.


Vectors have many uses from cross products in three dimensional space to multivariate random variables in statistics; as well as, applications in computer science. More commonly referred to as a Vector this geometric entity has many names: Euclidean, Geometric, & Spatial vectors.  A vector is a physical quantity represented by an arrow that has a magnitude and a direction.  Magnitude is the numerical value in physical units represented by the tail of the arrow.  The larger the magnitude the longer the tail. The direction  is at times given or easily interpretative   In physics, you should be careful with using intuition.  The best way to determine direction is to look at the signs (positive or negative) in which positive quantities move up or right and negative quantities move down or left.


When faced with any problem to solve, I encourage my students to always list the constants and variables (both known and unknown) first.  In physics, I require this first step. Second, you label each item as a vector or scalar quantity. Then we exercise the right side of the brain by drawing the object in the given environment and diagramming the physical quantities involved.  If you are not interested in exercising your artistic side, simply draw a square or circle to represent the object is acceptable. Below is a simple example. We will study difficult analysis as we investigate the human body in motion.

e.g. A ball with a mass of 0.5 kg is dropped 2 meter in 3 seconds with negligible air resistance.  
  • mass (m) = 0.5 kg ---> Scalar
  • distance (d) = 2m ---> Scalar
  • drag (Fair) = + .0000634 N ---> Vector
  • time (t) = 3 s ---> Scalar
  • weight (Fgrav) = (0.5) * (-9.8m/s^2) = - 4.9 N ---> Vector
By using a vector diagram it is easy to see how different forces affect the given object.  In the above example, the force of gravity is stronger than the force of air resistance. we can predict the motion of the ball by comparing the tails of each vector. The longer vector represents the stronger force.  Gravity will overcome the air resistance and the ball will fall until contacting the grounds. Vector diagrams can be used to observe the direction and magnitude of any vector quantity including velocity, acceleration, gravity, friction, applied force, etc. 


Now the you understand a basic vector analysis, you are ready to explore the various vectors that create and resist movement.  In this blog, I will break down many dance moves using vector diagrams. By looking at our activities analytically, you will better understand what makes a move difficult.  In more advanced diagrams, we will see how angles affect a given object which will help us visualize the proper body mechanics of movement from walking to dancing.   

No comments:

Post a Comment