Rotational Dynamics of Rigid Solids

Rotational Dynamics of Rigid Solids - Rotational Dynamics...

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Unformatted text preview: Rotational Dynamics of Rigid Solids C George Kapp 2002 Rev 2008 Table of Contents Page 1. Introduction.........................................................................…2 2. Coordinate System...................................................................4 3. Circular to Angular Transformations........................................4 4. The Cause Variable..................................................................6 5. Mathematical Interlude. ..........................................................8 6. Angular Relationships; The Strategy. .....................................10 7. Cause and Effect....................................................................10 8. Moment of Inertia, a Macro Quantity......................................12 9. Newton’s Second Law for Rotation. ........................................12 10. Angular Impulse and Momentum. .........................................14 11. Energy Relationships; The Strategy. ......................................15 13. Work; An Alternative View. ....................................................16 14. Parallel Axis Theorem.............................................................16 15. Rotational Equilibrium...........................................................17 16. Examples...............................................................................19 17. Appendix I, Moment of Inertia Computations.........................27 18. Appendix II. The Combination Method for determining the Total Kinetic Energy…………………….……………37 Rotational Dynamics of Rigid Solids 1 Introduction. It is this author’s intent to start with the laws of Newton, applied to a collection of particles, and deduce all laws of rotation. To provide a crystal clear path from one to the next. In consideration of this journey, the student must be aware that the basis for true understanding and clarity is as much a mater of perspective and interpretation, as it is an exercise in mathematics and the application of fundamental laws of nature. front cm axis Y axis Consider the above situation: We have a rigid block. We give it a 180 degree rotation about each of the two axes shown, the center of mass axis, and the Y axis which is parallel to the cm axis. For the cm axis, the result is, back cm axis Y axis back and for the Y axis, the result is, Y axis We compare the result of each operation. Many observers would consider the results as dissimilar – truly visual inspection would agree. The cm rotation produces no translation of the center of mass of the box whereas the Y rotation produces considerable displacement of the center of mass of the box. And yet, BOTH were 180 degree rotations. A mater of perspective and interpretation....
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This note was uploaded on 01/17/2011 for the course PHY PHY 211 taught by Professor Kapp during the Spring '10 term at Washtenaw.

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Rotational Dynamics of Rigid Solids - Rotational Dynamics...

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