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written9 - Homework 9 Due 1 Consider an isolated sphere of...

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Homework 9 Due March 20 2007 1) Consider an isolated sphere of uniform density of mass M and radius R 1 which rotates with a period of T 1 . a) Suppose that the sphere contracts so that it is now a sphere of radius R 2 < R 1 but it contracts in such a way that it is still of uniform density. What is the ratio T 2 / T 1 between the new period T 2 and the initial period T 1 ? What conservation law did you use to derive this result? b) If K rot1 is the rotational kinetic energy before the contraction and K rot2 the kinetic energy of rotation after the contraction, what is the ratio K rot2 / K rot1 ? c) Suppose that R 2 = R 1 - h where h << R 1 . Show that the above ratios can be approximated by 2 1 1 2 1 1 1 2 1 2 T h T R K h K R + (hint: see Text Section Appendix B page A3): d) A neutron star with a mass of twice that of the Sun and radius of 10 km rotates 30 times each second. What is its period in seconds? (A neutron star realistically can be modeled as a uniform, solid sphere) Calculate the rotational kinetic energy of the neutron star. (Note that the result you obtain is greater than the entire energy output of the Sun during its 10 billion year lifetime!)
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