Kinematics Unit 1

Objective To understand the concept of motion and how it has evolved through time. To understand the vocabulary associated with motion. To discern the difference between a scalar and a vector quantity. To understand how to illustrate motion through the process of graphing data.

Vocabulary Acceleration Motion Average Speed Motion diagram Circular Motion Position Constant Acceleration Relative Motion Displacement Scalar Frame of Reference Speed Function Time Graph Vector Linear Motion Velocity

Motion What is motion? It is the action or process of moving or being moved

Relative motion Relative motion is the calculation of the motion of an object with regard to some other moving object. Think of it like sitting in a car on the freeway. If you are driving at 70 mph and another car passes you going 80 mph, it would seem like you are standing still and the other person is moving away from you at 10 mph.

Who was the first person to study and try to explain the concept of motion?

Aristotle Aristotle, born in 384 B.C. in Stagira, in Thrace, at the northern end of the Aegean, near Macedonia Aristotle was a famous Greek philosopher, scientist, and educator. He was an adept student at Plato’s Academy, where Plato often referred to him as the "intellect: of the school. Many of his theories can be seen as drawn from Plato's teaching, but he was more practical in many respects. Aristotle concerned himself more with how philosophy applied to subjects like writing, the arts, science, and logic.

Aristotle method 1. defining the subject matter 2. considering the difficulties involved by reviewing the generally accepted views on the subject, and suggestions of earlier writers 3. presenting his own arguments and solutions.

Aristotle motion Every modern child has since birth seen cars and planes moving around, and soon finds out that these things are not alive, like people and animals. In contrast, most of the motion seen in fourth century Greece was people, animals and birds, all very much alive. This motion all had a purpose, the animal was moving to someplace it would rather be, for some reason, so the motion was directed by the animal's will. For Aristotle, this motion was therefore fulfilling the "nature" of the animal, just as its natural growth fulfilled the nature of the animal.

Aristotle motion To account for motion of things obviously not alive, such as a stone dropped from the hand, he extended the concept of the "nature" of something to inanimate matter. He suggested that the motion of such inanimate objects could be understood by postulating that elements tend to seek their natural place in the order of things, so earth moves downwards most strongly, water flows downwards too, but not so strongly, since a stone will fall through water. In contrast, air moves up (bubbles in water) and fire goes upwards most strongly of all, since it shoots upward through air. This general theory of how elements move has to be elaborated, of course, when applied to real materials, which are mixtures of elements. He would conclude that wood, say, has both earth and air in it, since it does not sink in water.

Aristotle motion Of course, things also sometimes move because they are pushed. A stone's natural tendency, if left alone and unsupported, is to fall, but we can lift it, or even throw it through the air. Aristotle termed such forced motion "violent" motion as opposed to “natural” motion. The term "violent" here connotes that some external force is applied to the body to cause the motion.

Aristotle motion (elements)

Even though Aristotle was not exactly correct in his explanation of motion, he started the process of looking at how and why things move. From this, the study of kinematics arrived.

Kinematics What is kinematics? It is the branch of mechanics concerned with the motion of objects without reference to the forces that cause the motion. The study of how and not why objects move.

How objects move We use the following words to describe motion. position reference point frame of reference time velocity (speed with a direction) acceleration displacement (distance)

Position Position – separation between object and a reference point. 

Reference point / frame of reference Reference point: zero location in a coordinate system or frame of reference. Frame of reference: coordinate system used to define motion.

Reference point / frame of reference Frame of reference: The City of Grand Rapids and the surrounding suburbs. Reference point: City High School. I live about 17 miles southeast of City High, therefore the position of my house is 17 miles southeast of City High.

Time Motion occurs over a period of time (time interval) or at an instant point in time. Time interval: difference in time between two clock readings. Time A nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future.

Velocity (speed) Velocity – the ratio of change in position to time interval over which change takes place (with a direction) •change in position – displacement • change in position in linear motion with no backward motion – distance Speed - the ratio of change in position to time interval over which change takes place (without a direction)

Vector vs. Scalar Scalar – quantity, like speed, that has only a magnitude, or size. Vector quantity – quantity, like velocity, having both magnitude (size) and direction. Speed – 30 km/hr Velocity – 30 km/hr north

Acceleration Acceleration – change in velocity divided by time interval over which it occurred. (meters / seconds2) change in position divided by time interval divided time interval (or simply change in position over time squared). (meters / seconds2) Constant acceleration – is an acceleration that does not change with time. The increase/decrease in velocity stays the same throughout the motion.

Displacement vs. distance What is displacement? Displacement: change in position. A vector quantity. How far away you are from where you were.

What is distance. Distance: separation between two points What is distance? Distance: separation between two points. A scalar quantity. How far away something is with respect to something else.

Distance = displacement B 5 km. Going from point A to point B is 5 km. The distance from point A to point B is 5 km. The displacement from point A to point B is 5 km.

Distance = displacement When is distance equal displacement? Distance equals displacement when we have linear motion where there is no backward motion.

Linear motion vs. circular motion Linear motion – motion in a straight line (aka. 1 dimensional) Circular motion – motion with constant radius of curvature caused by acceleration being perpendicular to velocity. Think of whirling a yo-yo. If the string breaks, the yo-yo would fly away in a straight path.

perpendicular radius

Distance ≠ displacement Distance = 5 km. + 2 km. = 7 km. A 5 km. B 3 km. C 2 km. Displacement = 5 km + (-2 km) = 3 km.

Distance ≠ displacement Distance = 4 + 3 = 7 km A 4 km B 3 km 5 km Displacement = √ 42 + 32 = √ 16 + 9 = √ 25 = 5 km C

Motion diagram We will use three graphs to show motion. These are called motion diagrams (as seen in the running man computer simulation). Displacement (distance) vs. time Velocity (speed) vs. time Acceleration vs. time.

Displacement vs. time graphs Negative acceleration Decreasing velocity 0 acceleration Constant velocity Positive acceleration Increasing velocity displacement 0 velocity Constant position time Reference point (the zero displacement) (starting point)

Velocity vs. time graphs Decreasing acceleration Constant acceleration Increasing acceleration velocity 0 acceleration Constant velocity time Reference point (the zero displacement) (starting point)

Acceleration vs. time graphs Increasing acceleration acceleration Constant acceleration Decreasing acceleration time Reference point (the zero displacement) (starting point)