2191. The Rock and Roll Telescope (Using a Gravitational Pendulum to Determine Moment of Inertia)

Paper

Abstract

Page 19.7 of the SAWE handbook, upper right, shows a method of measuring moment of inertia of a test item using a pendulum. The formulae presented in that figure work only when the pendulum rocks through a small angle. This paper presents an extension of that concept using a pendulum that is supported on a round cross section trunnion in such a way that the test item is simultaneously rocking and rolling. The technique described was actually used in measuring the CG and moment of inertia of a space bound telescope, as described in SAWE paper number 1945. The derivation of the small angle formula is presented. The concept is then extended by deriving the equation for the period NOT assuming a small angle. I chose 45 degrees as an example and worked through the equation. Finally, the implications for moment of inertia measurement are examined. Important Appendix 1. While working out this paper, the author began discovering various errors in the SAWE handbook. There are 160 errors listed. The work was checked by George Strom, who added several of his own findings. Both arc presented. Of these, 47% are misspellings and minor cosmetic defects, the remainder being actual erroneous formulas and factors. Some of this remaining 53% are in rather critical places, such as two erroneous conversion factors in the density units section, page 1.8. Important Appendix 2. This appendix presents an Excel spreadsheet of the formulas in section 4.x.x of the SAWE handbook. The author describes how to embed artwork into a spreadsheet to make the output look identical to section 4 of the handbook. With input of dimensions, the spreadsheet calculates the mass properties of the figure. The package was originally proposed as the San Francisco chapter project. The author intends to offer the package free to SAWE members at the 94 International Conference.