Chapter 10 Rotational Kinematics and Energy - SFSU Physics …wman/phy111hw/lecture notes... ·...
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Chapter 10 Rotational Kinematics and Energy
Transcript of Chapter 10 Rotational Kinematics and Energy - SFSU Physics …wman/phy111hw/lecture notes... ·...
Chapter 10
Rotational Kinematics and Energy
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 (Not required)
10-1 Angular Position, Velocity, and Acceleration
10-1 Angular Position, Velocity, and Acceleration
Degrees and revolutions:
10-1 Angular Position, Velocity, and Acceleration
Arc length s, measured in radians:
10-1 Angular Position, Velocity, and Acceleration
10-1 Angular Position, Velocity, and Acceleration
10-1 Angular Position, Velocity, and Acceleration
10-1 Angular Position, Velocity, and Acceleration
10-2 Rotational Kinematics
If the angular acceleration is constant:
10-2 Rotational Kinematics
Analogies between linear and rotational kinematics:
10-3 Connections Between Linear and Rotational Quantities
10-3 Connections Between Linear and Rotational Quantities
10-3 Connections Between Linear and Rotational Quantities
10-3 Connections Between Linear and Rotational Quantities
This merry-go-round has both tangential and centripetal acceleration.
10-4 Rolling MotionIf a round object rolls without slipping, there is a fixed relationship between the translational and rotational speeds:
10-4 Rolling MotionWe may also consider rolling motion to be a combination of pure rotational and pure translational motion:
10-5 Rotational Kinetic Energy and the Moment of Inertia
For this mass,
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
Use this equation to calculate I, for a few point masses.
10-5 Rotational Kinetic Energy and the Moment of Inertia
Moments of inertia of various regular shapes can be calculated using these known results:
Summary of Chapter 10• Describing rotational motion requires analogs to position, velocity, and acceleration
• Average and instantaneous angular velocity:
• Average and instantaneous angular acceleration:
Summary of Chapter 10
• Period:
• Counterclockwise rotations are positive, clockwise negative
• Linear and angular quantities:
Summary of Chapter 10
• Linear and angular equations of motion:
Tangential speed:
Centripetal acceleration:
Tangential acceleration:
Summary of Chapter 10
• Rolling motion:
• Kinetic energy of rotation:
• Moment of inertia for a few points:
• Moment of inertia for different shapes……
• Kinetic energy of an object rolling without slipping:
• Optional: When solving problems involving conservation of energy, both the rotational and linear kinetic energy must be taken into account.
10-6 Conservation of Energy
Optional Not RequiredThe 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.
10-6 Conservation of EnergyIf 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.
