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## Chapter 2

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**Chapter 2**Linear Kinematics Describing Objects in Motion**Define Motion:**• Motion is a change in position over a period of time. SpaceandTime**Types of Motion**• Linear Motion (translation) • all points on the body move • the same distance • in the same direction • at the same time • Rectilinear and Curvilinear**Linear Motion**• Rectilinear Translation: straight line • figure skater gliding across the ice**Linear Motion**• Curvilinear Motion: curved line • free-fall in sky-diving • Simultaneous motion in x & y directions • Horizontal and vertical motion superimposed**Types of Motion**• Angular Motion (rotation) • All points on the body move • through the same angle • Whole body rotation • giant swing, pirouette • Segment rotation • flexion, abduction, …**Types of Motion**• General Motion • combines angular & linear motion • most common • pedaling a bike • walking • drawing a straight line**Linear Kinematics**• Study of the time and space factors of motion**Linear Kinematic Quantities**• Kinematics is the form, pattern, or sequencing of movement with respect to time. • Kinematics spans both qualitative and quantitative form of analysis.**Linear Kinematic Quantities**• For example, qualitatively describing the kinematics of a soccer kick entails identifying • the major joint actions, • including hip flexion, • knee extension, • and possibly plantar flexion at the ankle.**Linear Kinematic Quantities**• A more detailed qualitative kinematic analysis might also describe the precise sequencing and timing of body segment movements, which translates to the degree of skill evident on the part of the kicker.**Linear Kinematic Quantities**• Although most assessments of human movement are carried out qualitatively through visual observation, quantitative analysis is also sometimes appropriate.**Linear Kinematic Quantities**• Physical therapists, for example, often measure the range of motion of an injured joint to help determine the extent to which range of motion exercises may be needed.**Linear Kinematic Quantities**• When a coach measures an athlete's performance in the shot put or long jump, this too is a quantitative assessment.**Linear Kinematics**• Description of Linear Motion • How far? • What direction? • How fast? • Speeding up, slowing down?**Position**• Identifying location in space • At the start of movement? • At the end of movement? • At a specific time in the midst of movement? • Use a fixed reference point • 1 dimension • starting line, finish line • 2 dimension • Bloomington-Normal: north, east, south, west • (goal line, sideline), (0,0), Cartesian coordinate system**Cartesian Coordinate System**Z direction X direction (0,0,0) Y direction**Linear Kinematic Quantities**• Constructing a model performance. • Scalar and vector quantities.**Linear Kinematic Quantities**• Displacement - change in position. • Distance - distance covered and displacement may be equal for a given movement or distance may be greater than displacement, but the reverse is never true.**Vector & Scalar Quantities**• Scalar: Fully defined by magnitude (how much) • Mass • Vector: Definition requires magnitudeand direction • Force**Distance and Displacement**• Measuring change in position • component of motion Distance = 1/4 mile Displacement = 0 Start and finish**Distance and Displacement**• Another example: • Football player (fig 2.2, p 51): • receives kickoff at 5 yard line, 15 yards from the left sideline • runs it back, dodging defenders over a twisted 48 yard path, to 35 yard line, 5 yards from the left sideline**Distance and Displacement**• Distance • length of path traveled: 48 yards • Displacement • straight line distance in a specified direction • y direction: yfinal - yinitial • x direction: xfinal - xinitial**Distance and Displacement**• Resultant Displacement • length of path traveled in a straight line from initial position to final position • y direction: yfinal - yinitial • x direction: xfinal - xinitial Components of resultant displacement R2 = (x)2 + (y)2**Distance and Displacement**• Resultant Displacement • length of path traveled in a straight line from initial position to final position • y direction: yfinal - yinitial • x direction: xfinal - xinitial Components of resultant displacement R2 = (x)2 + (y)2 = arctan (opposite / adjacent)**Assign**x & y coordinates to each of the markers (digitize)**Speed and Velocity**• For human gait, speed is the product of stride length and stride frequency. • Runners traveling at a slow pace tend to increase velocity primarily by increasing SL. • At faster running speeds, recreational runners rely more on increasing SF to increase velocity.**Speed and Velocity**• Most runners tend to choose a combination of stride length and SF that minimizes the physiological cost of running.**Speed and Velocity**• The best male and female sprinters are distinguished from their less-skilled peers by extremely high SF and short ground contact times, although their SL are usually only average or slightly greater than average.**Speed and Velocity**• In contrast, the fastest cross-country skiers have longer-than-average cycle lengths, with cycle rates that are only average.**Speed and Velocity**• Pace is the inverse of speed. • Pace is presented as units of time divided by units of distance (6 min/mile) • Pace is the time taken to cover a given distance and is commonly quantified as minutes per km or mins. per mile.**Speed and Velocity**• Acceleration - rate of change in velocity. • Acceleration is 0 whenever velocity is constant. • Average velocity is calculated as the final displacement divided by the total time period. • Instantaneous velocity - occurring over a small period of time.**distance**Speed = time Speed and Velocity • Measuring rate of change in position • how fast the body is moving • Speed • scalar quantity • how fast meters seconds**Examples**• Who is the faster runner: • Michael Johnson • 100m in10.09s • 200m in 19.32s (world record) • 300m in 31.56 s • 400m in 43.39s (world record) • Donovan Bailey (Maurice Greene) • 50m in 5.56 s (world record) • http://www.runnersweb.com/running/fastestm.html**Instantaneous Speed**• We have calculated average speed • distance by time to cover that distance • Maximum speed in a race? • make the time interval very small • 0.01 second or shorter**Speed and Velocity**• Measuring rate of change in position • how fast the body is moving • Speed • Velocity • vector quantity • how fast in a specified direction displacement m velocity = time s**Example**• Swimmer • 100 m race in 50 m pool • 24s and 25s splits • Calculate velocities & speeds • first length, second length • total race (lap)**Example**• Football player (fig 2.2, p 54): • receives kickoff at 5 yard line, 15 yards from the left sideline • runs it back, dodging defenders over a twisted 48 yard path, to 35 yard line, 5 yards from the left sideline • time is 6 seconds • Calculate velocities & speeds • forward, side to side, resultant**Use speed to calculate time**• Running at 4 m/s • How long to cover 2 m? • 2 m ÷ 4 m/sec= .5 sec