Angles - Let's treat them squarely

American Journal of Physics

Volumn 65, Issue 7, 1997, Pages 605-614

  Brownstein, K R ^a  

^a University of Maine   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031492101     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18616     Document Type: Article

References (33)

1. H. Young, University Physics (Addison-Wesley, Reading, MA, 1992), 8th ed., p. 354.
2. x where x has dimensions, say, of length.
3. C. H. Page, "Classes of Units in the SI," Am. J. Phys. 46, 78-79 (1978).
4. J. deBoer, "Group Properties of Quantities and Units," Am. J. Phys. 47, 818-819 (1979).
5. C. H. Page, "Rebuttal to de Boer's 'Group Properties of Quantities and Units,'" Am. J. Phys. 47, 820 (1979).
6. B. L. Scott, "Letter to the Editor," Am. J. Phys. 53, 520 (1985).
7. E. S. Oberhofer, "What Happens to the 'Radians'?," Phys. Teach. 30, 170-171 (1992).
8. W. E. Eder, "Rotary Motion and SI," Eur. J. Eng. Educ. 4, 319-327 (1980).
9. W. E. Eder, "A Viewpoint on the Quantity 'Plane Angle'," Metrologia 18, 1-12 (1982).
10. A. P. French, "What Happens to the 'Radians'?," Phys. Teach. 30, 260-261 (1992).
11. G. J. Aubrecht II, A. P. French, M. Iona, and D. W. Welch, "The Radian - That Troublesome Unit," Phys. Teach. 31, 84-87 (1993).
12. A. P. French, "Use and Misuse of the Radian in Angular Mechanics" (unpublished, ca. 1991).
13. R. D. Stiehler, "Getting the Right Angle," ASEE News 5(2), 3 (1978).
14. K. R. Brownstein, "Radian Measure in Mathematics and Physics," ASEE Annual Conference Proceedings (American Society for Engineering Education, Washington, DC, 1988), pp. 2117-2119.
15. K. R. Brownstein, "Concept of Angle as a Dimensional Quantity," AAPT Announcer 21(2), 92-93 (May, 1991).
16. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed., pp. 813-817.
17. B. L. Scott, "It's Obvious - Now," Phys. Teach. 31, 262 (1993).
18. R. A. Nelson, The International System of Units (American Association of Physics Teachers, College Park, MD, 1982), 2nd ed., p. 64.
19. J. B. Brinsmade, "Plane and Solid Angles, Their Value When Introduced Explicitly," Am. Phys. Teach. 4, 175-179 (1936). Brinsmade's development departs from that of the present article in that, e.g., his units for torque are dyn·cm/rad similar to those of Eder. (The American Physics Teacher later became The American Journal of Physics.)
20. -1, etc.
21. 2= 1, that the SI unit for cos(θ) is 1, and that the SI unit for sin(θ) is itself radian.
22. For computer usage, this might cause difficulty if there is no upper/lower case distinction. One may want to use an appropriate prefix or suffix, e.g., gsin for Sin, gcos for Cos, etc.; the prefix g connoting geometric. Of course one might argue that the "ordinary" geometric functions be left unchanged as far as notation is concerned and the notation for the mathematical trigonometric functions should be changed.
23. Phase velocity is perhaps the most descriptive name to assign to Ω, for Ω is the time rate of change of the phase (which is itself dimensionless). Unfortunately, the name phase velocity traditionally has a previous meaning. We suggest phase rate as a possible name for Ω.
24. Unfortunately, the traditional symbol T for the period (which has the dimensions of time) is also the symbol for the dimension T of time itself.
25. The use of a special name for a unit in a particular physical situation is not new. For example, we refer to a Newton·meter as a joule for energy but not for torque.
26. The "radius" of the reference circle has the same dimensions as that of the amplitude B; these need not, in general, be those of length.
27. D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics (Wiley, New York, 1993), 4th ed., p. 479.
28. R. Resnick, D. Halliday, and K. Krane, Physics (Wiley, New York, 1992), 4th ed., p. 421.
29. A "Rube Goldberg" device is an overly complicated machine designed to perform a simple task. It was popularized in an American cartoon.
30. R. A. Nelson, in Ref. 18, pp. 30-34.
31. Very recently, the 20th Conférence Générale des Poids et Mesures chose to eliminate the class of supplementary units and decided to interpret both the radian and steradian as dimensionless derived units. This does not alter the thrust of the present article. I am indebted to D. A. Blackburn for pointing out this change in the SI official interpretation to me.
32. As mentioned previously, we associate the non-SI angular unit "rev" with the symbol f.
33. We suggest the name phase gradient for K to parallel the suggestion of phase rate for Ω.