Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley PowerPoint ® Lectures for University Physics, Twelfth Edition – Hugh D. Young and Roger A. Freedman Lectures by James Pazun Chapter 3 Motion in Two or Three Dimensions

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Position relative to the origin—Figure 3.1 An overall position relative to the origin can have components in x, y, and z dimensions. The path for a particle is generally a curve.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Average velocity—Figure 3.2 The average velocity between two points will have the same direction as the displacement.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Components of velocity—Figure 3.5 A velocity in the xy-plane can be decomposed into separate x and y components. Trigonometry will aid the determination. Refer to Example 3.1.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The acceleration vector—Figure 3.6 The acceleration vector can result in a change in either the magnitude OR the direction of the velocity. Consider the race car in Figure 3.6.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Average and instantaneous acceleration—Example 3.2 Figure 3.9 shows velocity and acceleration as time passes. Study the robotic rover of Example 3.1 again.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Consider the different vectors—Figure 3.12 Notice the acceleration vector change as velocity decreases, remains the same, or increases.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Parallel and perpendicular components of acceleration Refer to the worked Example 3.3. Figure 3.13 illustrates the calculation in the example.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Skiing through a valley—Example 3.4 Conceptual Example 3.4 follows a skier going down, through a curve, and starting back up a hill. Figure 3.14 shows situation and solution.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Projectile motion—Figure 3.15 A projectile is any body given an initial velocity that then follows a path determined by the effects of gravity and air resistance. Begin neglecting resistance.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley X and Y motion are separable—Figure 3.16 The red ball is dropped, and the yellow ball is fired horizontally as it is dropped. The strobe marks equal time intervals.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The equations of motion under constant acceleration Projectile motion sets x o = 0 and y o = 0 then obtains the specific results shown at right. x = (v o cosα o )t y = (v o sinα o )t  1/2gt 2 v x = v o cosα o v y = v o sinα o  gt

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The effects of wind resistance—Figure 3.20 Cumulative effects can be large. Peak heights and distance fall. Trajectories cease to be parabolic.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Conceptual Example 3.5 Refer to Problem-Solving Strategy 3.1. Figure 3.21 illustrates the example (our friend the skier again).

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Throwing from a mound or chipping to a green This could be a tee shot or a military mortar. Whatever the case, launch angle is important. Follow Example 3.9. Refer to Figure 3.25.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Tranquilizing the falling monkey Where should the zookeeper aim? Follow Example 3.10.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Motion in a circle—Figure 3.27 The vehicle could be speeding up in the curve, slowing down in the curve, or undergoing uniform circular motion.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Finding motion information—Figure 3.28 Velocity change, average acceleration, and instantaneous acceleration may be found.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Determination of the centripetal acceleration Uniform circular motion and projectile motion compared and contrasted. For uniform circular motion, the acceleration is centripetal. Refer to Figure Follow Examples 3.11 and 3.12.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Nonuniform circular motion—Figure 3.30 If the subject’s speed varies? Radial and tangential components of the acceleration can grow and diminish with reasonable regularity.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Relative velocity—Figures 3.31 and 3.32 Fighter jets do acrobatic maneuvers moving at hundreds of miles per hour relative to the crowd but are nearly stationary with respect to each other. A conductor and a passenger on a moving train may both be moving at a rapid clip toward their destination, yet, the conductor can still move toward your seat to check your ticket.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Relative velocity on a straight road—passing! This could be a controlled pass of a slightly faster vehicle or a scary head-on approach. Follow Example Refer to Figure 3.33.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Relative velocity in two or three dimensions Back to the conductor approaching your seat on a moving train. Imagine a cyclist observing as she approaches the train. Refer to Figure 3.34.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Flying to the right or wrong airport An oblivious pilot can end up off course; an apt one steers on the “wrong” direction to end up at the desired destination. Follow Examples 3.14 and Refer to Figures 3.35 and 3.36.