Kinematics Description of MotionAccording to a website from Zonaland, Kinematics is defined as the science of motion. Motion explains how things move.
For better understanding, it is good to have a brief background on how motion was studied by humans. In a website from gbp.org, Aristotle, a Greek Philosopher, had claimed that all object fall in a constant speed. However, he had tried to explain why lighter objects such as a feather falls slower to earth.
He had explained that a feather falls slowly because he believes that the feather wants to return to the air, which is according to him, the feather’s resting place. Galileo had questioned this belief and had made experiments and tested the theories of Aristotle. He had made more accurate conclusions because of his controlled experiments. The theory of Aristotle that all objects move in a constant speed was also disproved by Galileo.
According to Galileo, objects falls faster as it gets near the earth. Another scientist that has made a very large impact in the science of Kinematics is Sir Isaac Newton. Sir Isaac Newton developed theories about motion and Inertia.Newton had stated three laws of motion in his work “Principia Mathematica Philosophiae Naturalis” in 1686.
The first law is that “Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it.” NASA states that this definition of motion can be said as the definition of Inertia. In layman’s term, if there is no external force exerted to a moving object then the object will maintain a constant velocity. If the velocity is zero then the object will remain at rest.
Figure 1 shows an application of Newton’s First Law. The figure was taken form NASA’s websiteFigure 1. Application of Newton’s First LawThe second law of motion is that “Force is equal to the change in momentum (mV) per change in time. For a constant mass, force equals mass times acceleration where F = m x a”.
NASA interpreted that the second law of motion explains how the velocity of an object changes when it is subjected to an external force. The law further explains that a force is equal to change in momentum per change in time. Momentum is defined as mass multiplied velocity. It could also be stated that for an external applied force, the change in velocity will depends on the mass of the object because force is subjected depending on its mass and acceleration.
A force causes velocity to change and a change in velocity generates a force. Figure 2 shows an application of the Newton’s second Law of Motion, this was taken from NASA’s website.Figure 2. Newton’s Second Law of MotionThe third law of motion states that “For every action, there is an equal and opposite reaction”, In order to easier understand this, NASA provided an explanation of two objects exerting forces.
When Object A exerted force to Object B, this means that Object B had also exerted an equal force to Object A.Figure 3. Newton’s Third LawSince Kinematics is the study of motion, it is imperative to know the common terms used. Among these terms are Displacement, Gravitational Acceleration, speed, instantaneous velocity, and average velocity.
When an object moves, an objet is in motion. If the object has changed its position from its original coordinates, this means that the object had incurred Displacement. According to Barnes and Noble, displacement is an object’s total change of position. An example given by Barnes and Noble is a man running in an oval for 400 km, he started running at a particular spot and stopped at the spot where he started.
The person’s displacement is considered zero because the person did not change the location where he has started. However, it can be noted that the man had ran for 400 meters. This means that the distance travelled by the person is 400 meters. The next term is the Gravitational Acceleration.
Gravitational Acceleration can be defined as the speed of a falling object. Barnes and Noble stated that gravitational acceleration is the same for all objects regardless of mass. The computed gravitational acceleration of objects according to scientists is 9.8m/s2.
Instantaneous Velocity is the value of the velocity at a certain given time where as the average velocity is the time average of the velocity function at a certain time arrival. Velocity is computed using the displacement and the time consumed by a particular object. Using, algebraic equations, the distance travelled and the time consumed can be computed using the primary formula of velocity. Figure 4.
Representation of Time Period, Constant Velocity and DisplacementThe first formula shows the formula of displacement. Where displacement can be computed using the velocity multiplied by the time the object had travelled. The second formula shows the formula for velocity. Velocity is computed using displacement divided by the time travelled and lastly, the third formula shows the formula of time travelled.
Time can be computed using the displacement of the object divided by the velocity.If a particular object is moving in the same interval of distances, in the same interval of time then the said object is moving in a constant acceleration. This means that the speed or velocity of the object is the same at any given point in time. When an object is moving in different interval of distances, in the same interval then the object is said to be a different acceleration.
The faster the object the higher the velocity and the slower the object gets the smaller the velocity. When an object becomes faster the distance covered in the intervals of time gets bigger as time goes by. Zonaland’s website had noted again that if a velocity is positive then this means that the displacement is positive. Velocity of the follows the direction of the displacement.
There are different types of motion under Kinematics. First is the one-dimensional motion. This type of motion is a motion that moves in a straight line. Zonaland website had described this type of motion as a motion moving only in the x-axis.
A forward motion indicates a positive motion this is so because in the x-axis, if a particular number is in the right then it is in the positive side. On the other hand, the backward motion is indicates a negative motion, because this motion moves to the left where the negative numbers in the x-axis lies. However, motion of a particular object does not only involve one spatial dimension. Second type is the two dimensional motion.
An object can move in several directions. Since there is a two-dimensional motion, scientist had used the vector to represent the direction of motion. According to the physics in a classroom website, the vector is described by the magnitude and direction. Vectors are represented by scalar diagrams in a quadrant.
These diagrams are used to determine the forces acting upon an object. These diagrams are also known as the free-body diagram. There are different directions that a vector can take. It could either move towards the south, north, east and west.
However, some are directed northeast or southwest and the like, In order to identify which particular slanting direction the vector is heading to, conventions were created. Conventions show the direction of an arrow and use an angle of rotation to demonstrate the specific direction. This angle is often expressed as a counterclockwise rotation from the east.Within the vector diagram, an arrow is drawn to represent the vector.
The arrow has a tail and a head. The magnitude of the arrow is represented by its length. A particular scale is use to represent the magnitude by the length of the arrow. An example of a vector diagram is shown in below.
Figure 5. Vector DiagramKinematics in human movement, is the study of the positions, angles, velocities, and accelerations of body segments and joints during motion. University of Vienna’s website defined several terms relating to the kinematics of the human motion. As defined in the website, Body segments are considered to be rigid bodies for the purpose of describing a motion.
These segments include the foot, shank (leg), thigh, pelvis, thorax, hand, forearm, upper-arm and head. Joints are the points where the body segments are connected.A joint angle is also considered. This is the angle between the two segments on either side of the joint.
Segment Angles are the angle of the segment with respect to the right hand horizontal. Velocity and acceleration are also important in the stud of Kinematics in the human movement.In the study for human motion, Kinematic motions give limited information on the causes of motion. In order to further understand, humans formulated kinetics.
However, kinematic motions describe the motion.Application of the study of motion can be seen in everyday life and throughout the history of man. Before, people used to walk to travel from one place to another. This is an application of the one-dimensional kinematics.
As the years passed by, the bicycle was invented. This had sped up travelling from travelling on foot to travelling on two wheels. But then again, people needed more time to do more things so the bicycle evolved into a car. Other transportation vehicles such as the airplane and the boat had also used the study of motion to further sped up travelling time of people.
According to Novak and Gavrin, engineers and scientists had applied physical principles to push the limits of mechanical devices. People and goods travelled anywhere be it the land the water and the sea because of this innovations. In the nineteenth century, mechanical devices were self-propelled and these were powered by heat engines. James Watt and the other scientists during his time had tried to replace animal power through fossil fuel power.
This had started the creation of steamboats, automobiles and trains.Nowadays, speeding had become a sport. Races had started to emerged. More and more complicated mechanical devices are assembled by engineers in order to reach the number one spot.
Because of speed, people would like to be known as the fastest car racer in the world or the fastest car invented.The two-dimensional Kinematics application can be seen in the industry of travelling. When people are travelling, people must know where they came from and where their destination is. Before people used marks in order to determine if they are in the right direction or not.
According to a website of Physics Giancoli, mapping had started because of travelling. Mapping the earth had become a necessity. Numerous people had worked on this in order to have an accurate map for travel. Hipparchus, a scientist twenty two thousand years ago, had proposed the clever coordinate system that we still use today.
A number of vector diagrams are used to represent the position of coordinates.Figure 6. Latitude and the LongitudeThe figure above demonstrates the Latitude and the Longitude. Two-dimensional perpendicular lines are used in order to determine the direction of a place.
Hipparchus had proposed angular separation between the two lines from the equator to a certain place. This is what we call the Latitude in the globe. The line passing through the Latitude of the earth is called the Meridians or Longitude. The zero meridian or prime meridian of the earth is the Greenwich Observatory of London.
After much study and contemplation, every point of the earth is now uniquely defined by its latitude and longitude.As a conclusion, Kinematics is a very powerful tool that had led to advancement of technology and innovations now. By studying further the concepts of these, scientists and engineers are still carrying out experiments to improve applications of these such as increasing air travel, water travel and land travel. Works CitedBarnes & Noble,” Introduction to Motion in Two and Three Dimensions”, 2D Motion Study Guide, 2006, Sparknotes LLC, 15 August 2007, <http://www.sparknotes.com/ physics/kinematics /2dmotion/summary.html>Benson, Tom, “Newton’s Law of Motion”, National Aeronautics And Space Administration, 14 March 2006, NASA First Gov, 15 August 2007, http://www.grc.nasa.gov/ WWW/K-12/airplane/rotations.htmlZobel, Edward, “The Physics Department-Kinematics, Mechanics”, 1997-2006, Zonaland, 15 August 2007, <http://id.mind.net/~zona/mstm/physics/mechanics/kinematics/ kinematics.html>“Kinematics”,15 August 2007 <http://www.univie.ac.at/cga/teach-in/kinematics.html?>University of Vienna, “Vectors-Fundamental and Operations”, 15 August 2007 <http://www.physicsclassroom.com/Class/vectors/U3L1a.html>Novak, Gregor and Gavrin Andrew, “Applications: Speed”, Indiana University-Purdue Unversity, 15 August 2007, <http://wps.prenhall.com/esm_giancoli_physicsppa_6 /0,8713,1113788-,00.html>