Formation of a Neutron StarA star rotates with a period of 32 days about an axis through its center. The period is the time interval required for a point on the star's equator to make one complete revolution around the axis of rotation. After the starundergoes a supernova explosion, the stellar core, which hadradius of 1.1 x 104 km, collapses into a neutron star of radius 3.6 km. Determine the period of rotation of the neutron star.SOLUTIONConceptualize The change in the neutron star's motion is similar to that of the skater described earlier in the textbook, but in the reverse direction. As the mass of the star moves closer to the rotation axis, we expectthe star to spin fasterCategorize Let us assume that during the collapse of the stellar core, (1) no external torque acts on it, (2) it remains spherical with the same relative mass distribution, and (3) its mass remains constant. We categorizesystem in terms of angular momentum. We do not know the mass distribution of the star, but we have assumed the distribution is symmetric, so the moment of inertia can be expressedthe star as an isolatedas KMR2, where k is some numerical constant. (From this table, for example, we see that k =for a solid sphere and k =for a spherical shell.)Analyze(Use the following as necessary: w, T, Tp R, Rp, k, and M.)Let's use the symbol T for the period, with T, being the initial period of the star and T, being the period of the neutron star. The star's angular speed is given by w =T.From the isolated system model for angular momentum, write the following equation for the star:oI = 'm'IUse w = 27/T to rewrite this equation in terms of the initial and final periods:Substitute the moments of inertia in the preceding equation:kMR,kMR,Solve for the final period of the star:Tf =R;Substitute numerical values to find the final period (in s):Tf =Finalize The neutron star does indeed rotate fasterafter it collapses, as predicted.It moves very fast, in fact, rotating (in rotations per second)times each second.EXERCISEA solid metal sphere of diameter D is spinning in a gravity-free region of space with an angular velocity of w. The sphere is slowly heated until it reaches its melting temperature, at which point it flattens into a uniformdisk of thickness 2. By what factor is the angular velocity changed? (Give your answer as a factor of w,.)Hint

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EXERCISE A solid metal sphere of diameter D is spinning in a gravity-free region of space with an angular velocity of w. The sphere is slowly heated until it reaches its melting temperature, at which point it flattens into a uniform disk of thickness 2. By what factor is the angular velocity changed? (Give your answer as a factor of w.) Hint

EXERCISE A solid metal sphere of diameter D is spinning in a gravity-free region of space with an angular velocity of w. The sphere is slowly heated until it reaches its melting temperature, at which point it flattens into a uniform disk of thickness 2. By what factor is the angular velocity changed? (Give your answer as a factor of w.) Hint

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter12: Rotation I: Kinematics And Dynamics

Section: Chapter Questions

Problem 15PQ

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