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

© 2016 Pearson Education, Inc.

A New Way to Measure Angular Quantities – Figure 9.2 •  The radian, defined.

© 2016 Pearson Education, Inc.

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.

© 2016 Pearson Education, Inc.

We Have a Sign Convention – Figure 9.7

© 2016 Pearson Education, Inc.

Comparison of Linear and Angular – Table 9.1

© 2016 Pearson Education, Inc.

Rotation of a Bicycle Wheel – Figure 9.8

•  See Example 9.2 in your text.

© 2016 Pearson Education, Inc.

Kinematics Can Relate Linear and Angular –Figure 9.9 •  Refer to Quantitative Analysis 9.2.

© 2016 Pearson Education, Inc.

The Bicycle and Discus – Example 9.3

•  See Conceptual Analysis 9.3.

•  The examples shown in Figures 9.11 and 9.12

© 2016 Pearson Education, Inc.

An Airplane Propeller – Example 9.4

•  Refer to Figure 9.13 and the worked problem on page 264.

© 2016 Pearson Education, Inc.

Bicycle Gears – Figure 9.15

•  See the worked example at the bottom of page 265.

© 2016 Pearson Education, Inc.

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.