Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and...
-
Upload
edgar-hunter -
Category
Documents
-
view
222 -
download
0
Transcript of Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and...
![Page 1: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/1.jpg)
Chapter 10
Rotational Kinematics and Energy
![Page 2: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/2.jpg)
Units of Chapter 10• Angular Position, Velocity, and Acceleration
• Rotational Kinematics
• Connections Between Linear and Rotational Quantities
•Rolling Motion
• Rotational Kinetic Energy and the Moment of Inertia
• Conservation of Energy
![Page 3: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/3.jpg)
10-1 Angular Position, Velocity, and Acceleration
![Page 4: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/4.jpg)
10-1 Angular Position, Velocity, and Acceleration
Degrees and revolutions:
![Page 5: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/5.jpg)
10-1 Angular Position, Velocity, and Acceleration
Arc length s, measured in radians:
![Page 6: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/6.jpg)
10-1 Angular Position, Velocity, and Acceleration
![Page 7: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/7.jpg)
10-1 Angular Position, Velocity, and Acceleration
![Page 8: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/8.jpg)
10-1 Angular Position, Velocity, and Acceleration
![Page 9: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/9.jpg)
10-1 Angular Position, Velocity, and Acceleration
![Page 10: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/10.jpg)
10-2 Rotational Kinematics
If the angular acceleration is constant:
![Page 11: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/11.jpg)
10-2 Rotational Kinematics
Analogies between linear and rotational kinematics:
![Page 12: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/12.jpg)
10-3 Connections Between Linear and Rotational Quantities
![Page 13: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/13.jpg)
10-3 Connections Between Linear and Rotational Quantities
![Page 14: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/14.jpg)
10-3 Connections Between Linear and Rotational Quantities
![Page 15: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/15.jpg)
10-3 Connections Between Linear and Rotational Quantities
This merry-go-round has both tangential and centripetal acceleration.
![Page 16: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/16.jpg)
10-4 Rolling MotionIf a round object rolls without slipping, there is a fixed relationship between the translational and rotational speeds:
![Page 17: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/17.jpg)
10-4 Rolling Motion
We may also consider rolling motion to be a combination of pure rotational and pure translational motion:
![Page 18: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/18.jpg)
10-5 Rotational Kinetic Energy and the Moment of Inertia
For this mass,
![Page 19: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/19.jpg)
10-5 Rotational Kinetic Energy and the Moment of Inertia
We can also write the kinetic energy as
Where I, the moment of inertia, is given by
![Page 20: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/20.jpg)
10-5 Rotational Kinetic Energy and the Moment of Inertia
Moments of inertia of various regular objects can be calculated:
![Page 21: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/21.jpg)
10-6 Conservation of Energy
The total kinetic energy of a rolling object is the sum of its linear and rotational kinetic energies:
The second equation makes it clear that the kinetic energy of a rolling object is a multiple of the kinetic energy of translation.
![Page 22: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/22.jpg)
10-6 Conservation of Energy
If these two objects, of the same mass and radius, are released simultaneously, the disk will reach the bottom first – more of its gravitational potential energy becomes translational kinetic energy, and less rotational.
![Page 23: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/23.jpg)
Summary of Chapter 10
• Describing rotational motion requires analogs to position, velocity, and acceleration
• Average and instantaneous angular velocity:
• Average and instantaneous angular acceleration:
![Page 24: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/24.jpg)
Summary of Chapter 10
• Period:
• Counterclockwise rotations are positive, clockwise negative
• Linear and angular quantities:
![Page 25: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/25.jpg)
Summary of Chapter 10
• Linear and angular equations of motion:
Tangential speed:
Centripetal acceleration:
Tangential acceleration:
![Page 26: Chapter 10 Rotational Kinematics and Energy. Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections Between.](https://reader036.fdocuments.us/reader036/viewer/2022062407/56649e8a5503460f94b8f640/html5/thumbnails/26.jpg)
Summary of Chapter 10
• Rolling motion:
• Kinetic energy of rotation:
•Moment of inertia:
• Kinetic energy of an object rolling without slipping:
• When solving problems involving conservation of energy, both the rotational and linear kinetic energy must be taken into account.