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Chapter 9 Lecture
Chapter 9: Rotational Motion
© 2016 Pearson Education, Inc.
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.
© 2016 Pearson Education, Inc.
Rigid Bodies Can Rotate Around a Fixed Axis – Figure 9.1
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A New Way to Measure Angular Quantities – Figure 9.2 • The radian, defined.
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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 2 radians = 360º.
• Try to convert some common angles (45º, 90º, 360º).
© 2016 Pearson Education, Inc.
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 , the angular velocity.
• Consider Figure 9.4 and Conceptual Analysis 9.1.
© 2016 Pearson Education, Inc.
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 , the angular acceleration.
© 2016 Pearson Education, Inc.
Determine the Rotation of a Compact Disk –Example 9.1 • Refer to Example 9.1 in your text.
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We Have a Sign Convention – Figure 9.7
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Comparison of Linear and Angular – Table 9.1
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Rotation of a Bicycle Wheel – Figure 9.8
• See Example 9.2 in your text.
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Kinematics Can Relate Linear and Angular –Figure 9.9 • Refer to Quantitative Analysis 9.2.
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The Bicycle and Discus – Example 9.3
• See Conceptual Analysis 9.3.
• The examples shown in Figures 9.11 and 9.12
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An Airplane Propeller – Example 9.4
• Refer to Figure 9.13 and the worked problem on page 264.
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Bicycle Gears – Figure 9.15
• See the worked example at the bottom of page 265.
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Rotational Energy – Example 9.6
• Refer to Figure 9.16 and the worked problem on page 267.
© 2016 Pearson Education, Inc.
Moments of Inertia & Rotational Energy – Example 9.7 • Example 9.7 makes
use of Table 9.2. • See the detailed
solution on page 269 and in Figure 9.18.
© 2016 Pearson Education, Inc.
A Rotation While the Axis Moves – Example 9.9 • The example refers to
Figure 9.22. • See the detailed
solution on page 272.
© 2016 Pearson Education, Inc.
Race of the Rolling Objects – Example 9.10
• Refer to Figure 9.23 and the detailed solution on page 272.
© 2016 Pearson Education, Inc.