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Kinematics Review

Kinematics Review. Kinematics Review a) Exam information b) What kind of questions? c) Review. First Midterm Exam on Friday. Covers Units 1-3 plus “Math” One-dimensional Kinematics Two-Dimensional Kinematics Relative and Circular Motion Unit conversion Trigonometry and Algebra

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Kinematics Review

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  1. KinematicsReview Kinematics Review a) Exam information b) What kind of questions? c) Review

  2. First Midterm Exam on Friday • Covers Units 1-3 plus “Math” • One-dimensional Kinematics • Two-Dimensional Kinematics • Relative and Circular Motion • Unit conversion • Trigonometry and Algebra • 50 minute duration • Multiple choice • Calculators Allowed/Needed • Three sheets of notes.(equivalent font size>9)(this is font size=9)

  3. What type of questions? • Interpretation and use of graphs Which of the following statements about the velocity of the cart is correct? What is the velocity at t=? What is the acceleration at t= ? ….

  4. What type of questions? • Displacement, velocity and acceleration in 1 dimension Given some combination of acceleration, initial velocity, final velocity, displacement, elapsed time, etc. calculate an unknown quantity using the kinematic equations….

  5. What type of questions? V0=0m/s H=10m V1 ground • Motion with constant acceleration in 1-dimension Given some combination of acceleration, initial velocity, final velocity, displacement, elapsed time, etc. calculate an unknown quantity using the kinematic equations….

  6. What type of questions? • Relative motion in 2 dimensions Given some combination of relative velocity between frames of reference answer questions related to the displacement and elapsed times for certain actions…

  7. What type of questions? • Projectile motion Given some combination of initial velocity, range , maximum height, etc…calculate characteristics of projectile motion..

  8. What type of questions? N E m R Top view • Circular Motion Given some combination of angular velocity, Radius, ac calculate a characteristic of the motion of an object at constant speed in a circle…

  9. What type of questions? • Any material from Units 1-3 • Calculations • Unit conversion • Algebra, trigonometry and vectors • Conceptual Questions • Similar to pre-lecture and checkpoint questions

  10. What type of questions? • Vectors q • Decompose a vector into polar or Cartesian coordinates • Vector Addition (Subtraction)

  11. How to prepare? • Read the textbook • Review the video prelectures • Review the lecture slides • (Re-)Work homework problems • Prepare three sheets of notes • Basic Fundamental Equations • Derived Equations( and be able to derive them!) • Unit conversions • Algebra notes (quadratic equation) • Trigonometric relations • Vector concepts • Conceptual notes,… • Get enough sleep!!!

  12. Main Points of Unit 1

  13. Main Points of Unit 1

  14. Vectors and 2d-kinematics – Main Points

  15. Vectors and 2d-kinematics – Main Points

  16. Vectors and 2d-kinematics Important Equations

  17. Relative and Circular Motion a) Relative motion b) Centripetal acceleration

  18. HyperphysicsMotion Displacement vstimet Velocity vstimet Acceleration vstimet

  19. HyperphysicsMotion

  20. 1d-Kinematic Equations for constant acceleration • Basic Equations to be used for 1d – kinematic problems. • Need to apply to each object separately sometimes with time offset • When acceleration changes from one constant value to another say a=0 The problem needs to be broken down into segments

  21. Maximum Height of ball thrown upward in gravitational field What is the velocity of an object when it is at its maximum height? Two ways to solve for maximum height… Solve for position directly Solve for time first Remember a is negative Use tf to solve for maximum height…

  22. The meeting Problem Whenever possible solve symbolically. Then plug in the numbers!!!! You can understand what is going on better if you keep the equations organized. Define your problem; Identify useful equations Start solving… Gather terms…Does the equation look reasonable? Solve for desired quantity… Position of object 1 when object 2 is launched This time is w.r.t object 2. To obtain time w.r.t object 1 need to add delay time Speed of object 1 when object 2 is launched

  23. Break problem into parts Region 1: 0<t<1.5 s Region 2 Region 1 Region 3 Region 2: 1.5s<t<3.0s What happened in region 3? Region 3: 3.0s<t<5.0s Smartphysics Conclusion

  24. 2d-Vectors q Think of a vector as an arrow. (An object having both magnitude and direction) The object is the same no matter how we chose to describe it

  25. Algebra and Trigonometry • Algebra • Algebra is “fair” • Quadratic Equation • Trigonometry

  26. Vector Addition Add Components!!! AddTail to Head

  27. Kinematics in 3D

  28. Projectile Motion Vertical Horizontal Boring

  29. Ballistic Projectile Motion Quantities Initial velocity speed,angle Maximum Height of trajectory, h=ymax “Hang Time” Time of Flight, tf Range of trajectory, D Height of trajectory at arbitrary x,t

  30. Derived Projectile Trajectory Equations Maximum height Time of Flight (“Hang Time”) Range of trajectory Height of trajectory as f(t) , y(t) Height of trajectory as f(x), y(x)

  31. Relative Motion in 2 Dimensions Speedrelative to shore

  32. Relative Motion in 2 Dimensions Direction w.r.t shoreline

  33. Centripetal Acceleration • Constant speed in circular path • Acceleration directed toward center of circle • What is the magnitude of acceleration? • Proportional to: • Speed • time rate of change of angle or angular velocity v = wR

  34. Additional Slides

  35. Once around: v = Dx /Dt = 2pR / T w = Dq /Dt = 2p / T v = wR wis the rate at which the angleqchanges: q

  36. v = wR Another way to see it: v dt =R dq dq R v = Rw

  37. Two thrown balls problem #2 Use your equation in symbolic form and gather the values to be used…. Solve for individual elements of equation…can check if things make sense Position of object 1 at moment object 2 is launched Velocity of object 1 at moment object 2 is launched Solve for displacement and relative velocity at time when object 2 launches Note that acceleration term after 2nd object is released drops out!!! Divide to obtain time when objects meet

  38. Homework Hints – Stadium Wall Calculate time to reach wall using vx: Calculate y position at time to reach wall:

  39. Homework Hints – Stadium Wall Calculate time to reach wall using vx: Calculate y position at time to reach wall:

  40. Homework Solutions-Baseball Stadium

  41. Plane Ride N E East of north

  42. Car on Curve

  43. Maximum Height of Trajectory Height of trajectory,h=ymax

  44. Time of Flight, “Hang Time”

  45. Range of trajectory

  46. Angle for Maximum Range MAXIMUM range OCCURS AT 450

  47. Height of Trajectory at time t or position x Height of trajectory, y(t) Height of trajectory, y(x)

  48. Launch Velocity-Given R and 

  49. Launch Angle

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