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Review sessions (both in NPB 1001, i.e. here): Thursday, Sept. 9 th (Hill), 6:15-8:10pm

IMPORTANT NOTICES. 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) Exam 1 – Mon. Sept. 13, 8:20-10:20pm

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Review sessions (both in NPB 1001, i.e. here): Thursday, Sept. 9 th (Hill), 6:15-8:10pm

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  1. IMPORTANT NOTICES • Review sessions (both in NPB 1001, i.e. here): • Thursday, Sept. 9th (Hill), 6:15-8:10pm • Friday, Sept. 10th (Woodard), 6:15-8:10pm • Subject: chapters 1-4 (similar coverage each night) • Exam 1 – Mon. Sept. 13, 8:20-10:20pm • (Important instructions for exam in Fri./Mon. classes) 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 Position: • Coefficients x, y, and z give the particle's coordinates relative to the origin. Displacement: • 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.

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

  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: • Instantaneous velocity: • Or:

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

  8. Projectile motion • 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. • 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.

  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. • 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 x0 and y0

  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

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