Mechanics - The Study of Motion

Kinematics - Describing Motion

 

Unit I Kinematics Scientificic Method Notes One D Problem Set One D Homework - pdf One D Homework - Word
Physics 500 Physics 500 Summary   Quiz 1 Quiz 1
Moving Plot Formuas Moving Plot Notes Moving Plot 1 Video Setting up the Data/Results Table Quiz 2 Quiz 2
  Video Using The Equation Editor to do sample calculations Moving Plot 2 Video Setting Up Graphs Quiz 3 Quiz 3
      Quiz 4 Quiz 4

 


In this unit we will be using some new vocabulary and math techniques to describe motion.  In Natrual Physics we will only work in one dimension.  All we are concerned with at this time is describing motion, not the causes of motion.  The causes of motion will come later.

Vocabulary:

Displacement:  Many people think of displacement as distance.  As is common in science words have very specific meanings and those meanings may not be the same as in general society.  Distance is the measurement of space between two points.  Nothing has to happen for there to be a distance.  Displacement requires movement, a change in position, an object going from one place to another.  Direction is required for displacement but the direction is often assumed or implied.  Displacement in the metric system is measured in meters and the symbol in the math equations that we use is x.

Velocity:  Velocity is the slope of the displacement vs. time graph.  Many people think of velocity as speed.  The major difference is that velocity has direction as part of the measurement, either expressed ( 20 m/s North) or implied (falling at 3.2 m/s).  For people with higher math skills, velocity is the rate of change in position or the first derivative of position.  Velocity in the metric system is measured in meters/second and the symbol in the math equations we use is v.

Acceleration:  Acceleration is the slope of the velocity vs. time graph.  Acceleration always has direction although in common usage people often us deceleration as a term for negative acceleration.  It is the second derivative of position or the rate of change of velocity.  Acceleration is measured in meters/second/second (meters per second squared) and the symbol in the math equations we use is a.

Jerk:  The jerk is a physics quantity that is seldom used in formal physics but the concept is often used in general society.  The jerk is the slope of the acceleration vs. time graph.  Because any measurement errors are already greatly magnified in acceleration, calculating a value for jerk often results in errors that are greater than the values calculated.

Time:  Something that we all know about but is difficult to define.  In classical physics the change in time is constant.  We may define the beginning of time how ever we want but time does not stop, speed up, slow down or end.  Time in the metric system is measured in seconds and the symbol in the math equations we use is t.

Slope:  Many people define slope as "the rise over the run".  While this is a true statement I think it loses much of the beauty of the math.  Slope as a formula is calculated as (y2-y1)/(x2-x1).  Producing graphs and being able to estimate the slope of the graph are great tools to get a "big picture" view of the motion of objects.  It is also an abstract thinking skill that takes many students a long time to master.  A major focus on the first part of this unit will be on creating and analyzing these graphs.

Independent variable:  In this section of physics, time is always the independent variable, the quantity that does not depend on anything else.  In classic math, the independent variable is always put on the x axis.

Dependent variable:  The variables that are determined by something else.  In the case of kinematics the independent variables depend on time.  Where you are, how fast you are moving, how your velocity is changing all depend on time, the time does not depend on you being somewhere (can you imagine time ceasing to exist because you weren't in your assigned seat during 1st block?).  The dependent variable is always put on the y axis.

Math Equations:

average velocity = ∆x/∆t                acceleration = ∆v/∆t              x= x0 + vx0∆t + 1/2 ax∆t2               2a∆x=vx2-vx2


Links:
The Physics Classroom
Human Kinematics - Future doctors, atheletes, nurses, physical therapists take note!
Kinematics Simulation at Thinkquest
Relative Motion Simulator Frame of Reference Demonstrated

Projectile Simulator