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Reviewing the Semester

This semester review covers key topics in physics, including Newton's Laws, conservation laws, wave phenomena, and statistical mechanics and thermodynamics. Topics such as kinematics, momentum, energy conservation, and gravitational applications are explored in depth. The review also delves into simple harmonic motion, waves, and the principles of statistical mechanics and thermodynamics, including Boltzmann distribution and the laws of thermodynamics. Understanding these fundamental concepts is crucial for mastering physics principles and applications.

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Reviewing the Semester

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  1. Reviewing the Semester • Began with Newton’s Laws • Had to develop language of kinematics first • Position, displacement, velocity, acceleration • Vectors, vector addition, multiplication • Inertial and non-inertial reference frames • Useful when the force is constant • Like gravity close to the earth:

  2. Reviewing the Semester • Non-constant forces • Integrating the force over space (line integral) leads to work and energy • For some forces, integral doesn’t depend on the path, just the end points; then we define the potential energy

  3. Reviewing the Semester • Non-constant forces • Integrating the force over time leads to momentum • Momentum allows us to deal with systems of particles because we can add all the momenta together • Newton’s 3rd Law allows us to neglect all the internal forces and treat the system as one object

  4. Reviewing the Semester • Systems of Particles • A rigid system of particles (and any other) can not only translate (momentum) but rotate • To deal with this, we developed angular kinematics and dynamics

  5. Reviewing the Semester • Conservation Laws • Energy, momentum, angular momentum aren’t just useful ways to deal with Newton’s Laws • They have a deep significance because they are conserved • Conservation laws are related to symmetries in nature • Momentum Conservation is related to translational symmetries (invariance, physics doesn’t depend on our choice of origin) • Energy Conservation is related to time invariance • Angular Momentum Conservation is related to angular invariance

  6. Reviewing the Semester • Applications of Newton’s Laws: Universal Gravitation • Central Force Motion

  7. Reviewing the Semester • Applications of Newton’s Laws: Universal Gravitation • Kepler’s Laws • Planets orbit in ellipses with sun at one focus • Planets sweep out equal areas in equal times: angular momentum conserved • Period-Orbit Size relationship

  8. Reviewing the Semester • Applications of Newton’s Laws: Simple Harmonic Motion • For systems where Hooke’s Law applies • Pendulums

  9. Reviewing the Semester • Applications of Newton’s Laws: Simple Harmonic Motion • When damping and/or forcing are present

  10. Reviewing the Semester • Applications of Newton’s Laws: Waves • Waves obey the wave equation • Transverse waves on a string • Harmonic solutions Don’t forget energy and power transmission!

  11. Reviewing the Semester • Applications of Newton’s Laws: Waves • Sound waves • Pressure vs displacement • Decibels • Doppler Shift

  12. Reviewing the Semester • Applications of Newton’s Laws: Waves • Standing waves • On a string • In an air column (closed at one end) • Interference • Waves of the same frequency but different phases • Constructive or destructive • Beats • Interference in time • Beat frequency is difference between two wave freq.

  13. Reviewing the Semester • Statistical Mechanics and Thermodynamics • Can’t follow each molecule explicitly • Average energy, temperature • State Equation for Ideal Gas

  14. Reviewing the Semester • Statistical Mechanics and Thermodynamics • Boltzmann Distribution • Probability for a given velocity (a vector!) goes as its energy • Maxwell-Boltzmann Velocity distribution • Probability to have a given magnitude for the velocity • More ways to make a big velocity than small

  15. Reviewing the Semester • Statistical Mechanics and Thermodynamics • 1st Law of Thermodynamics • Processes • Isochoric • Isobaric • Isothermal • Adiabatic

  16. Reviewing the Semester • Statistical Mechanics and Thermodynamics • 2nd Law of Thermodynamics • Can’t have heat flowing cold-to-hot without work • Can’t have heat changing completely to work without some being lost • Heat Engines • Work is area enclosed in cycle (on PV diagram) • Carnot cycle (isothermal & adiabatic) most efficient • Sterling cycle (isothermal & ischoric) • Equipartition Theorem

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