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Unformatted text preview: Homework Assignment 1 Physics 302, Classical Mechanics Fall, 2010 Ashutosh Kotwal Handed out: Friday, Sep. 3, 2010 Due in class on: Friday, Sep. 10, 2010 Problems 1. The figure below shows measurements of the speeds of orbiting gas clouds in the spiral galaxy NCG 3198 as a function of distance from the center of the galaxy. Let’s assume that the galaxy consists primarily of a giant sphere of “dark” matter. The density of this sphere is assumed to be spherically symmetric, but it may vary with radius. Let M ( R ) be the mass contained within this sphere out to a radius R . Find M (10kpc), M (20kpc), and M (30kpc). Express your answers in terms of the mass of the Sun ( M sun = 10 30 kg, 1kpc ≈ 3 . 1 × 10 19 m). (see: www.slac.stanford.edu/pubs/beamline/27/3/27-3-rosenberg.pdf) 2. Show that the total angular momentum of a system of N particles is the sum of the angular momentum of their center of mass and the relative angular momentum of the particles with respect to the center of the mass.of the mass....
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