Linear Kinematics Describing Objects in Motion

Define Motion: »Motion is...

Define Motion: »Motion is a change in position over a period of time. Space and Time

Types of Motion l Linear Motion (translation) »all points on the body move –the same distance –in the same direction –at the same time »Rectilinear Translation: straight lineRectilinear Translation –figure skater gliding across the ice »Curvilinear Motion: curved lineCurvilinear Motion –free-fall in sky-diving

Types of Motion l Linear Motion (translation) l Angular Motion (rotation) »all points on the body move –through the same angle »Whole body rotationWhole body rotation –giant swing, pirouette »Segment rotation –flexion, abduction, yada yada yada ….

Types of Motion l Linear Motion (translation) l Angular Motion (rotation) l General Motion »combines angular and linear motion »most common type of human movement –pedaling a bike –walking –drawing a straight line

Linear Kinematics l Description of Linear Motion »how far? »What direction? »How fast? »Speeding up, slowing down?

Position l Identifying location in space »at the start of movement? »At the end of movement? »At a specific time in the midst of movement? l 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

Recall: Vector & Scalar Quantities l Scalar: Fully defined by magnitude »mass l Vector: Definition requires magnitude and direction »force

Distance and Displacement l Measuring change in position »component of motion l Football player: »receives kickoff at 5 yard line, 15 yards from the left sideline »runs it back, deking defenders over a twisted 48 yard path, to 35 yard line, 5 yards from the left sideline

Distance and Displacement l Distance »length of path traveled: 48 yards l Displacement »straight line distance in a specified direction »y direction: y final - y initial »x direction: x final - x initial

Distance and Displacement l Resultant Displacement »length of path traveled in a straight line from initial position to final position –y direction: y final - y initial –x direction: x final - x initial Components of resultant displacement R 2 = (  x) 2 + (  y) 2

Distance and Displacement l Resultant Displacement »length of path traveled in a straight line from initial position to final position –y direction: y final - y initial –x direction: x final - x initial Components of resultant displacement R 2 = (  x) 2 + (  y) 2  = arctan (opposite / adjacent)

Speed and Velocity l Measuring rate of change in position »how fast the body is moving l speed »scalar quantity –how fast Speed = time distance

Speed and Velocity l Measuring rate of change in position »how fast the body is moving l speed »scalar quantity –how fast Speed = time distance meters seconds

Examples l Who is the faster runner: »Michael Johnson –100m in10.09s –200m in 19.32s (world record) –300m in s –400m in 43.39s (world record) »Donovan Bailey (Maurice Greene)Donovan Bailey –50m in 5.56 s (world record) »

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Instantaneous Speed l We have calculated average speed »distance by time to cover that distance l Maximum speed in a race? »Make the time interval very small » 0.01 second or shorter

Speed and Velocity l Measuring rate of change in position »how fast the body is moving l speed l velocity »vector quantity –how fast in a specified direction velocity = time displacement m s

Example l Swimmer »100 m race in 50 m pool »24s and 25s splits l Calculate velocities & speeds » first length, second length » total race (lap)

Example l Football player: »receives kickoff at 5 yard line, 15 yards from the left sideline »runs it back, deking defenders over a twisted 48 yard path, to 35 yard line, 5 yards from the left sideline l time is 6 seconds l Calculate velocities & speeds » forward, side to side, resultant

Use speed to calculate time l Running at 3 m/s l How long to cover 2 m?

Projectile Motion Click here to go to a site showing the predictability of projectile motion (applied kinematic equations) Or here for a site on the high jump.

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Quiz If a body is traveling in the + direction and it undergoes a – acceleration, the body will ____________________. If a body is traveling in the – direction and it undergoes a + acceleration, the body will ___________________. Speed up or slow down

Acceleration l Quantifying change of motion »speeding up or slowing down »rate of change of velocity Acceleration = velocity time v f - v i t f - t i =  

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