Designs and Measurements in Mechanics

  1. High temperature measurements using
    1. The Boltzmann probability distribution
      Example. (Balmer absorption lines) [Eis, pp.104-105, Example 4-7].
    2. Planck's radiation equation [Zem, p.446, (17-27)]
      Example. Optical pyrometer [Eis, p.19, l.19-l.20; Zem, §17-13].

  2. Refractive index [Jen, p.28, Fig.2D; p.32, l.1-l.3].

  3. Measuring the Fermi Surface.
    1. Using uniform magnetic fields [the de Haas - van Alphen effect] to measure extremal cross section areas [Ashc, p.274, (14.15)].
    2. Using the magnetoacoustic effect to measure extremal diameters [Ashc, p.277, (14.20)].

  4. Measuring magnetic-flux density
    1. using the torque exerted on the magnetic dipole [Jack, p.174, (5.1)].
    2. using the force between two current-carrying wires [Jack, p.178, l.12].

  5. The limits of generating and measuring electromagnetic waves [Dit, p.11, l.4-p.12, l.1].

  6. Measuring the wavelength of light using stationary waves [Dit, p.51, Fig. 3.13 (a) or (b); pp.56-57, §3.29].

  7. Measuring dielectric constant by placing the material within a capacitor [Hec, p.41, l.c., l.-22 & Sad, p.226, l.13].

  8. The act of measurement disturbs the preexisting state [p.55, l.-18-p.56, l.18].

  9. In a dielectric, we use a needlelike cavity to measure the electric field [Wangs, p.148, l.7-l.23] and use a disc-shaped cavity to measure the displacement [Wangs, p.152, l.-13-l.-1].

  10. Measuring magnetic fields by the Hall effect. It is better to use semiconductors instead of conductors because the former contain a smaller number of charge carriers [Hoo, p.446, l.-14].

  11. Electrical measuring instruments [Hall, pp.526-527, §29-6].
    1. The ammeter is a meter to measure currents.
    2. The voltmeter is a meter to measure potential differences.
    3. The potentiometer is a meter to measure electromotive force (i.e., the work that the seat of emf does on positive charge carriers).
    Remark. The key idea of these meters' design is to minimize disturbance in the state of the circuit.

  12. Measuring e/m for the electron [Hall, p.549, Fig. 30-12; p.550, (30-18)].

  13. Measuring the specific heat capacity [Iba, p.102, Fig. IV.1] and thermal conductivity [Iba, p.103, Fig. IV.3] of solids at low temperatures (down to 0.3 K).

  14. Measuring magnetic inductions with a magnetron [Wangs, p.542, Fig. A-8; p.543, (A-63)].
    Key idea: Decrease the potential difference between the two cylinders in [Wangs, p.542, Fig. A-8] so that there will be no current between the cylinders.

  15. Measuring large distances.
    1. The distance to the Andromeda Nebula [Pee, p.18, l.21-p.19, l.16].
      Key idea: The ratio of mass to luminosity for any star is the same as that for the sun.

  16. Measuring velocities via the redshift [Lid, p.9, l.19-20].
    Key idea: [Lid, p.9, (2.1) & (2.2)]. The equality given in [Lid, p.9, l.-3] can be derived from [Rob, p.21, (3.1b)].

  17. The age of the universe.
    1. Radioactive dating of the oldest rock found on earth, of meteorites, and of lunar material: 4.5 ´ 109 years [Ken, p.147, l.1].
    2. Using the relative abundance of pairs of 235U and 238U: 15 ´ 109 years [Ken, p.147, l.10].

  18. The cosmic distance hierarchy.
    Remark. The method we use to measure greater distances involves greater uncertainty [Ber, p.5, l.-6-l.-5].
    1. (~ 30 pc) Parallax [Ber, p.6, l.-5-p.p.8, l.3].
    2. Doppler shift [Ber, pp.8-9, §2.2.2].
      1. (~ 40.8 pc) The moving cluster method [Ber, p.9, l.6].
      2. (Several hundred pc) The method of statistical parallaxes [Ber, p.9, l.19].
    3. Distance from apparent luminosity.
      1. (~ 4´104 pc) Main-sequence stars [Ber, p.11, l.9-p.12, l.-11].
      2. (~ 4´106 pc) Cepheid variables [Ber, p.12, l.-10-p.14, l.4]
      3. (~ 4´107 pc) Novae [Ber, p.14, l.5-l.-11].
      4. (~ 8´109 pc) Brightest galaxies in clusters [Ber, p.14, l.-10-l.-1].
    Remark. 1 pc = 3.26 light-years.

  19. The measurements in a moving frame.
        Suppose a clock and a rod are at rest in the frame S and an observer is at rest in the frame S' moving away from the frame S with the velocity V. An event has space coordinates and a time coordinate. Suppose the observer measures the length of a rod. He must find the coordinates of the ends of the rod simultaneously [Lan2, p.11, l.18] and the measured length should not vary over time. Now suppose the observer measures the time interval between two signals issued by a fixed light source [Wangs, p.503, l.9-l.17]. In contrast to the previous example, for the observer in the frame S' only the time part of the difference of the two events is selected as the time elapsed even though the two events' space coordinates may differ. The time interval should have a unique value no matter where the clock is put in the frame S. In other words, the measurement of a physical quantity in the moving frame S' should preserve as many intrinsic properties of the quantity in the rest frame S as possible. In short, when measuring a length, the observer should keep the time coordinates of the two events in the frame S' the same; when the observer measures a time interval, the clock should be kept at the same position in the frame S. One of the reasons why special relativity is difficult to understand is that physicists fail to think thoroughly about the philosophy (the big picture and what stand one should take under a circumstance) behind the calculations.
    Remark 1. Landau's proof [Lan2, p.11, l.14-l.-9] of the Lorentz contraction is simpler and more direct than Wangsness' [Wangs, p.503, l.19-l.-5].
    Remark 2. The way in which the electromagnetic field tensor is resolved into electric and magnetic components is determined by the relative motion of the observer [Wangs, p.522, (29-139); l.-13-l.-12].

  20. Measuring the speed of a sound wave [Zem, p.121, l.10-l.17].

  21. Measuring heat capacity at constant pressure [Zem, p.81, l.19-p.82, l.3].

  22. Measuring CP/CV [Kem, p. 114, Fig.5-7; p.120, (5-12)].

  23. Measurement of vapor pressure [Zem, §10-6].

  24. Measuring the critical pressure, molar volume, and temperature [Zem, §13-3].

  25. Using experiments to verify Maxwell's equation for the distribution of molecular speeds [Zem, p.295, Fig. 11-7].

    1. Determining the Planck constant and the Boltzmann constant using the Planck radiation formula [Wu, p.35, l.14-l.15].
    2. Determining the Planck constant using the photoelectric effect [Eis, p.30, (2-3); p.31, l.18 & l.23; p.28, Fig. 2-3].

  27. The field-synthesis point of view makes it easier to grasp the essence of solving a design problem [Fan, p.6, l.-9-l.-3; p.11, l.10-l.18].

  28. Measuring the refractive index of a transparent substance using a prism [Hec, p.188, (5.54)].

  29. How Hertz created an electromagnetic wave and measured its speed [Fur, §1.4C3].

  30. The construction of a cycloidal pendulum [Cou2, vol. 1, p.411, l.-12-p.412, l.-1; p.428, l.1-p.430, l.4].

  31. For practical purposes it is convenient to characterize the state of polarization by Stokes parameters because these parameters can be determined from simple experiments [Born1, p.31, l.-13-l.-8].

  32. Fresnel's rhomb [Born1, p.54, Fig. 1.16]
    Usage: linearly polarized light « circularly polarized light
    Principle based on: total reflection
    Key idea of the design: adding equal angles.

  33. Roemer used Io's Jupiter eclipse to measure the speed of light
    Principle based on: The speed of light is finite.
    Key idea of the design: The period of Io circling around Jupiter is fixed, but its measurement from Earth may appear different because Earth may move either near or away from Jupiter.