Elementary Physics, Mechanics, and Acoustics

This appendix derives some basic results from the field of
*physics*, particularly *mechanics* and *acoustics*,
which are referenced elsewhere in this book, or which are known to be
needed in practical synthesis models.

- Newton's Laws of Motion

- Work and Energy
- Potential Energy in a Spring
- Kinetic Energy of a Mass
- Mass Kinetic Energy from Virtual Work
- Energy in the Mass-Spring Oscillator
- Energy Conservation
- Energy Conservation in the Mass-Spring System

- Momentum

- Rigid-Body Dynamics
- Center of Mass
- Translational Kinetic Energy
- Rotational Kinetic Energy
- Mass Moment of Inertia
- Perpendicular Axis Theorem
- Parallel Axis Theorem
- Stretch Rule
- Area Moment of Inertia
- Radius of Gyration
- Two Masses Connected by a Rod
- Angular Velocity Vector
- Vector Cross Product
- Angular Momentum
- Angular Momentum Vector
- Mass Moment of Inertia Tensor
- Principal Axes of Rotation
- Rotational Kinetic Energy Revisited
- Torque
- Newton's Second Law for Rotations
- Equations of Motion for Rigid Bodies

- Properties of Elastic Solids

- Wave Equation for the Vibrating String

- Properties of Gases
- Particle Velocity of a Gas
- Volume Velocity of a Gas
- Pressure is Confined Kinetic Energy
- Bernoulli Equation
- Bernoulli Effect
- Air Jets
- Acoustic Intensity
- Acoustic Energy Density
- Energy Decay through Lossy Boundaries
- Ideal Gas Law
- Isothermal versus Isentropic
- Adiabatic Gas Constant
- Heat Capacity of Ideal Gases
- Speed of Sound in Air
- Air Absorption

- Wave Equation in Higher Dimensions

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University