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Chapter 4:Kinematics in Two Dimensions

Chapter 4:Kinematics in Two Dimensions. 1.Two-Dimension Kinematics 2.Projectile Motion 3.Relative Motion 4.Uniform Circular Motion 5.Velocity and Acceleration in Uniform Circular Motion 6.Nonuniform Circular Motion.

JasminFlorian
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Chapter 4:Kinematics in Two Dimensions

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  1. Chapter 4:Kinematics in Two Dimensions 1.Two-Dimension Kinematics 2.Projectile Motion 3.Relative Motion 4.Uniform Circular Motion 5.Velocity and Acceleration in Uniform Circular Motion 6.Nonuniform Circular Motion

  2. Stop to think 4.1 P 93Stop to think 4.2 P 97Stop to think 4.3 P 102Stop to think 4.4 P 107Stop to think 4.5 P 110Stop to think 4.6 P 113 • Example 4.3 P97 • Example 4.4 P98 • Example 4.5 P100 • Example 4.6 P101 • Example 4.9 P106 • Example 4.13 P110 • Example 4.15 P114

  3. Position and Velocity

  4. Instantaneous velocity The Instantaneous velocity vector is tangent to the trajectory. The direction of the velocity is to the curve.

  5. Don’t confuse these two graphs

  6. Acceleration

  7. The instantaneous acceleration can bedecomposed into parallel and perpendicular components

  8. Stop to think:This acceleration will cause the particle to: • Speed up and curve upward • Speed up and curve downward • Slow down and curve upward • Slow down and curve downward • Move to the right and down • Reverse direction

  9. Projectile Motionobject moves in two dimensions under the gravitational force. B A • What is the accelerations at position A and B? • What is the velocities at position A and B?

  10. A projectile launched horizontally falls in the same time as projectile that is released from rest

  11. Plot of projectile motion in t-xy

  12. Launch angle

  13. Ex. A ball thrown horizontally at velocity Vi , travels a horizontal distance of R m before hitting the ground. From what height was the ball thrown?(1) Since ball is thrown horizontally, Vi =VxThere is no acceleration at x direction.ie. R = Vxt, t = R/Vx(2) Viy=0, h = -1/2gt2

  14. Problem 50 Solve a quadratic equation to get t

  15. The maximum height and distance of fly ball For projectile motion, always remember:

  16. Trajectories of a projectile launched at different angles with the same speed

  17. Relative Motion • Relative position Relative velocity

  18. Uniform Circular Motion • Period • Angular Position

  19. Angular Velocity • Average angular velocity =∆θ/∆t • Instantaneous angular velocity • The angular velocity is constant during uniform circular motion

  20. An old-fashioned single-play vinyl record rotates 30.0 rpm . What are (a) the angular velocity in rad/s and (b) the period of the motion? • rpm: revolution per minute. 1 rpm = 2π/60 (rad)/s

  21. Velocity and acceleration in uniform circular motion

  22. Velocity in uniform circular motion The magnitude of velocity is a constant Vt =r dθ/dt =ωr Has only a tangential Component

  23. Centripetal acceleration

  24. The magnitude of centripetal acceleration P184 Towards center of circle

  25. Velocity and acceleration in Uniform Circular Motion The velocity has only a tangential component Vt

  26. Nonuniform Circular Motion Change the speed Here α is angular acceleration

  27. Rotational kinematics • For constant angular acceleration

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