Transcript Slide 1
9 Rotational Motion Lectures by James L. Pazun Goals for Chapter 9 • To study angular velocity and angular acceleration. • To examine rotation with constant angular acceleration. • To understand the relationship between linear and angular quantities. • To determine the kinetic energy of rotation and the moment of inertia. • To study rotation about a moving axis. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Rigid bodies can rotate around a fixed axis. – Figure 9.1 Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley A new way to measure angular quantities - Figure 9.2 •The radian, defined. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Practice angular thinking, first with displacement. •Angular displacement – (radians, rad). – Before, most of us thought “in degrees”. – Now we must think in radians. Where 1 radian = 57.3o or 2p radians=360o . •Try to convert some common angles ( 45o, 90o, 360o). Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Continue angular thinking, now to velocity. •If we follow what we studied in mechanics, we moved from displacement to velocity •Radians per second will be our units for ω, the angular velocity. •Consider Figure 9.4 and the matched conceptual analysis, 9.1. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley We can complete our variables with acceleration. •If we follow our pattern from mechanics, we moved to changes of velocity which we called acceleration. •Radians per second squared will be the units for α, the angular acceleration. •Consider Figure 9.4 and the matched example that follows. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Determine the rotation of a compact disk – Example 9.1 • Refer to the worked example 9.1 in your text. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley We have a sign convention. – Figure 9.7 Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Comparison of linear and angular – Table 9.1 For linear motion with constant acceleration For a fixed axis rotation with constant angular acceleration a = constant α = constant v = vo + at ω = ωo + αt x = xo + vot + ½at2 Θ = Θo + ωot + ½ αt2 v2 = vo2 + 2a(x-xo) ω2 = ωo2 + 2α(Θ-Θo) x–xo = ½(v+vo)t Θ-Θo= ½(ω-ωo)t Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Rotation of a bicycle wheel – Figure 9.8 See worked example 9.2 in your text. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Kinematics can relate linear and angular. – Figure 9.9 • Refer to quantitiative analysis 9.2. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley The bicycle and discus – Example 9.3 • See the example worked through in conceptual analysis 9.3. • The examples shown in Figure 9.11 and 9.12. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley An airplane propeller – Example 9.4 Refer to the worked problem on pages 275-276. and figure 9.13. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Bicycle gears – Figure 9.15 •See the worked example at the bottom of page 276. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Rotational energy – Example 9.6 •Refer to the detail on page 278 and figure 9.16. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Moments of inertia & rotational energy – Example 9.17 •The problem shown in example 9.7 makes use of table 9.2. • See the detailed solution on page 280 and in figure 9.20. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley A rotation while the axis moves – Example 9.9 • The example refers to figure 9.22. • See the detailed solution on pages 280283. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Race of the objects on a ramp – Example 9.10 • This is a classic multiple-choice question from MCAT-style standardized tests. • Refer to the detailed solution on pages 283-284 and figure 9.23. Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley