1. Review sessions (both in NPB 1001, i.e. here):Review sessions (both in NPB 1001, i.e. here): Thursday, Sept. 9 th (Hill), 6:15-8:10pm Friday, Sept. 10 th (Woodard), 6:15-8:10pm Subject: chapters 1-4 (similar coverage each night)Subject: chapters 1-4 (similar coverage each night) Exam 1 – Mon. Sept. 13, 8:20-10:20pmExam 1 – Mon. Sept. 13, 8:20-10:20pm (Important instructions for exam in Fri./Mon. classes) IMPORTANT NOTICES Chapter 1 and 2 WebAssign homework deadlines are tonight at 11pm (chapter 3 on Friday, 11pm).

2. Class 7 - Motion in 2D and 3D Chapter 4 - Wednesday September 8th 2D/3D Position, displacement, velocity and acceleration Example problems Projectile motion, with demonstrations Example problems Reading: pages 58 thru 70 (chapter 4) in HRW Read and understand the sample problems Assigned problems from Chapter 4: 6, 8, 14, 20, 30, 40, 46, 52, 56, 62 (due Sun. 12th)

3. Position and displacement The equations of motion that we introduced in chapter 2 apply equally to two- and three-dimensional motion.The equations of motion that we introduced in chapter 2 apply equally to two- and three-dimensional motion. All we need to do is to break the motion up into components, and treat each component independently, i.e. we will have two sets of equations in 2D, and three sets in 3D.All we need to do is to break the motion up into components, and treat each component independently, i.e. we will have two sets of equations in 2D, and three sets in 3D. Coefficients x, y, and z give the particle's coordinates relative to the origin.Coefficients x, y, and z give the particle's coordinates relative to the origin. Position: Displacement:

4. Important note! In chapter 3, you were told that the sum of two displacement vectors is given as follows: Displacement vectors are added graphically by placing the tail of one vector at the head of the other.

5. Important note! Position vectors represent coordinates. The displacement between two position vectors is given by the difference between the ending position and the starting position: O

6. Average and instantaneous velocity In component form:In component form: Instantaneous velocity:Instantaneous velocity: Or:Or:

7. Average and instantaneous acceleration In component form:In component form: Instantaneous acceleration:Instantaneous acceleration: Or:Or:

8. Projectile motion Motion in a vertical plane where the only influence is the constant acceleration due to gravity.Motion in a vertical plane where the only influence is the constant acceleration due to gravity. In projectile motion, the horizontal motion and vertical motion are independent of each other, i.e. they do not affect each other.In projectile motion, the horizontal motion and vertical motion are independent of each other, i.e. they do not affect each other. This feature allows us to break the motion into two separate one-dimensional problems: one for the horizontal motion; the other for the vertical motion.This feature allows us to break the motion into two separate one-dimensional problems: one for the horizontal motion; the other for the vertical motion. We will assume that air resistance has no effect.We will assume that air resistance has no effect.

9. Examples of projectile motion

10. Demonstration

11. Back to projectile motion This demonstration, which I showed in class, illustrates the fact that vertical motion is unaffected by horizontal motion, i.e. the two balls accelerate at the same constant rate, irrespective of their horizontal component of motion.This demonstration, which I showed in class, illustrates the fact that vertical motion is unaffected by horizontal motion, i.e. the two balls accelerate at the same constant rate, irrespective of their horizontal component of motion. In all of the projectile motion problems that we will consider, we shall assume that the only acceleration is due to gravity ( a=-g ) which acts along the y - axis.In all of the projectile motion problems that we will consider, we shall assume that the only acceleration is due to gravity ( a=-g ) which acts along the y - axis.

12. Analyzing the motion Initial coordinates x 0 and y 0

13. Remember these formulae?

14. Horizontal motion

15. Vertical motion

16. Projectile equations of motion

17. The effects of air The physics professor's home run always goes further than the professional's