# UWL ESS 303 - Final Exam Study Guide (8 pages)

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## Final Exam Study Guide

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- Pages:
- 8
- Type:
- Study Guide
- School:
- University of Wisconsin-La Crosse
- Course:
- Ess 303 - Biomechanics

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ESS 303 1st Edition Final Exam Study Guide Linear Kinematics Linear in a straight line from point A to point B Angular rotational from angle A to angle B Kinematics VS Kinetics Kinematics description of motion without regard for underlying forces Acceleration Velocity Position Kinetics determination of the underlying causes of motion i e forces Linear Kinematics The branch of biomechanics that deals with the description of the linear spatial and temporal components of motion Describes transitional motion from point A to point B Uses reference systems 2D X Y axis 3D X Y Z axis Position location in space relative to a reference Scalars and vectors Scalar quantities described fully by magnitude mass distance volume etc Vectors magnitude and direction the position of an arrow indicates direction and the length indicates magnitude Distance the linear measurement of space between points Displacement area over which motion occurred straight line between a starting and ending point Speed distance per unit time distance time Velocity displacement per unit time or change in position divided by change in time displacement time Graph Basics SI Units Systeme International d Units Standard units used in science Typically metric Mass Kilograms Distance Meters Time Seconds Temperature Celsius or kalvin More Terms Acceleration change in velocity divided by change in time V t m s s 2 Acceleration of gravity 9 81m s Differentiation the mathematical process of calculating complex results from simple data e g using velocity and time to calculate acceleration Derivative the solution from differentiation Integration the opposite of differentiation e g calculation of distance from velocity and time Speed d t Velocity position t Acceleration V t Slope rise run 2 2 Resultant X Y 2 2 2 Remember A B C SOH CAH TOA Sin Y component hypotenuse Cos X component hypotenuse Tan Y component X component Sample Problems A swimmer completes 4 lengths of a 50m pool What distance was traveled What was the swimmer s displacement Move from point 3 5 to point 6 8 on a graph What was the horizontal displacement What was the vertical displacement What was the resultant displacement Sample Problems A runner accelerates from 0m s to 4 7m s in 3 2 seconds What was the runner s rate of acceleration Someone kicks a football so that it travels at a velocity of 29 7m s at an angle of 22 above the ground What was the vertical component of velocity What was the horizontal component of velocity Angular Kinematics The branch of biomechanics that deals with the description of the angular components of motion Uses degrees or radians to describe position and or movement Degree 360 in a circle Radian the length of 1 radius along the arc of a circle 1 radian 57 3 degrees Angular Kinematics In the drawing to the right A B C have the same angular displacement or rotation A B C have different linear displacements Angular Kinematics S R angle in radians S displacement along the arc R radius If radius A 1m radius B 2m radius C 3m and each had a rotation of 90 what were the displacements of each Angular Kinematics 90 1 57 radians SA 1 57rad 1m SA 1 57m SB 1 57rad 2m SB 3 14m SC 1 57rad 3m SC 4 71m Angle Types Relative angle between segments Absolute describes the orientation of an object in space Right Hand Rule Today s Formulas 1 radian 57 3 degrees S R remember to use radians here Tan Y Y X X proximal distal proximal distal Angular speed angular distance time Angular velocity t Angular acceleration t Problems A figure skater turns 6 times What was the angular distance traveled What was the angular displacement While watching a golf swing you note that the angular velocity at time 0 05s was 1 6 5rad s and at time 0 54s was 15 87rad s 2 What was the angular acceleration Projectiles Which Will Hit First Put Things Together 4 Steps Step 1 Calculate the X and Y components of movement V V Cos X0 0 V V Sin Y0 0 Step 2 Calculate the maximum height How far up did it go 2 2 Y V V 2a up Y Y0 Y How far down will it fall think about it down Put Things Together 4 Steps Step 3 Calculate the hang time 2 Y at t 2Y a Remember to add time up and time down Step 4 Calculate the range the horizontal distance X V t X0 Problems You drop a penny from the top of a 2000 meter high building How long will it take to hit the ground How fast will it be going when it hits Problems A player kicked a football giving it a velocity of 20m s at an angle of 37 It was caught by another player at a height of 1 5meters What were the X and Y components of velocity How high did it go How long was it in the air How far apart were the players Quiz 2 Notes Next week Bring a calculator with trig functions Formula sheet provided same as one on the web Scratch paper is recommended About 16 total points About 5 problems ranging in points from 2 to 7 Show your work and include units Quiz 2 Sample Problems A runner completes 17 laps of a quarter mile track What was his or her distance and displacement Distance 4 25 Miles Displacement 0 Miles Move on a grid from point 3 6 to point 8 10 What are your horizontal vertical and resultant displacements Horizontal Displacement 5 Vertical Displacement 4 Resultant Displacement 6 40 More Quiz 2 Sample Problems A ballerina twirls 4 times What was her angular distance in degrees and radians Angular Distance 1620 Degrees Angular Distance 28 27 Radians While watching a golf swing you note that the angular velocity at the 18 second mark was 2 5 radians second You also see that the angular velocity at the 41 second mark was 12 02 radians second What was the angular acceleration t 2 12 02 2 5 41 18 9 52 0 23 41 39 r s Final Quiz 2 Sample Problem A pitcher throws a ball 1 5 meters above the ground The ball is released at a 23 degree angle at a velocity of 37 m s How far down field will the ball go do all 4 steps and show your work Final Quiz 2 Sample Problem Step 1 Horizontal and Vertical Velocities V V Cos X 0 V 34 06 m s X V V Sin Y 0 V 14 46 m s Y Final Quiz 2 Sample Problem Step 2 How high did it go from point of release 2 2 Y V V 2 a y0 y1 Y 10 66 meters up Y 12 16 meters down Final Quiz 2 Sample Problem Step 3 What was the flight time t 2Y a t 1 47 seconds t 1 57 Seconds up down t 1 47 1 57 3 04 Seconds total Final Quiz 2 Sample Problem Step 4 How far down field did the ball …

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