1. © 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. Lecture PowerPoint Physics for Scientists and Engineers, 3 rd edition Fishbane Gasiorowicz Thornton

2. Chapter 3 Motion in Two and Three Dimensions

3. Main Points of Chapter 3 Position and displacement Velocity and acceleration Trajectories Motion with constant acceleration Projectile motion Uniform circular motion Relative motion

4. 3-1 Position and Displacement Measure position from origin of coordinate system Displacement vector is difference of two position vectors: (3-1)

5. 3-1 Position and Displacement Position vectors depend on origin of coordinate system, but displacement vector does not:

6. 3-2 Velocity and Acceleration Velocity is defined analogously to one-dimensional velocity: (3-5) (3-7)

7. 3-2 Velocity and Acceleration The velocity vector is tangent to the trajectory:

8. 3-2 Velocity and Acceleration Acceleration: Components: (3-18) (3-15)

9. 3-2 Velocity and Acceleration Velocity vector is tangent to x-t curve Acceleration vector has no simple relationship to x-t curve, but is tangent to v-t curve:

10. 3-3 Motion with Constant Acceleration Trajectory for projectile motion lies in the plane formed by the initial velocity vector and the acceleration vector Position and velocity for constant acceleration: (3-25) (3-26)

11. 3-4 Projectile Motion Projectile: Object moving with the acceleration of gravity Path lies in a plane x-component of the velocity is constant y-component is found using equations for constant acceleration Projectile is launched with initial speed v 0 at an angle θ 0.

12. 3-4 Projectile Motion Trajectory is a parabola Range is distance object travels over level ground Range depends on launch angle

13. 3-5 Uniform Circular Motion Object in uniform circular motion travels in circle at constant speed Describe motion by distance from center r, and angle from x-axis φ Arc length: (3-43)

14. 3-5 Uniform Circular Motion Instantaneous speed: (3-45) Define angular speed: Then: (3-47) (3-46)

15. 3-5 Uniform Circular Motion Acceleration: By looking at change in velocity vector, see that instantaneous acceleration points toward center of circle: Magnitude of acceleration can also be found: (3-56)

16. 3-6 Relative Motion Observers moving with respect to each other will describe motion differently:

17. Summary of Chapter 3 Position vector of particle moving in space: Velocity: (3-5) Instantaneous acceleration: (3-15) (3-3)

18. Summary of Chapter 3, cont. For constant acceleration: (3-25) (3-26) In absence of air resistance, projectile moves with constant acceleration near Earth’s surface

19. Summary of Chapter 3, cont. Uniform (constant speed) circular motion Arc length: (3-43) Instantaneous speed: (3-45) Angular speed: (3-47) (3-46)

20. Summary of Chapter 3, cont. Acceleration: (3-56) Relative motion: Observers disagree on velocities but agree on accelerations if relative velocity is constant (3-60)