**Formation of a Neutron Star**A star rotates with a period of 32 days about an axis through its center. The period is the time required for a point on the star’s equator to make one complete revolution around the axis of rotation. After the star undergoes a supernova explosion, the stellar core, which had a radius of \(1.1 \times 10^4 \, \text{km}\), collapses into a neutron star of radius 3.6 km. Determine the period of rotation of the neutron star.**Solution****Conceptualize**: 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 expect the star to spin faster.**Categorize**: 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 categorize the star as an isolated system 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 expressed as \(kMR^2\), where \(k\) is some numerical constant. (From this table, for example, we see that \(k = \frac{2}{5}\) for a solid sphere and \(k = \frac{2}{3}\) for a spherical shell.)**Analyze**(Use the following as necessary: \(\omega\), \(T_i\), \(T_f\), \(R_f\), \(R_i\), \(k\), and \(M\).)Let’s use the symbol \(T\) for the period, with \(T_i\) being the initial period of the star and \(T_f\) being the period of the neutron star. The star’s angular speed is given by \(\omega = \frac{2\pi}{T}\).From the isolated system model for angular momentum, write the following equation for the star:\[ I_i \omega_i = I_f \omega_f \]Use \(\omega = \frac{2\pi}{T}\) to rewrite this equation in terms of the initial and final periods:\[ I_i \left( \frac{2\pi

Since you have asked multiple questions, we will solve the exercise question for you. If you want any specific question to be solved then please specify the question number or post only that question.From the conservation of angular momentum. Initially, the rotating body was in the shape of a solid sphere. Thus, the moment of inertia be: Finally, the rotating body becomes a uniform disk. Thus, the moment of inertia be:The volume of the disk and sphere is the same. Thus, the relation between their radius be:Thus, after substituting the values in the expression of the conservation of momentum and solving further.

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Physics

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

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

**Formation of a Neutron Star**

A star rotates with a period of 32 days about an axis through its center. The period is the time required for a point on the star’s equator to make one complete revolution around the axis of rotation. After the star undergoes a supernova explosion, the stellar core, which had a radius of \(1.1 \times 10^4 \, \text{km}\), collapses into a neutron star of radius 3.6 km. Determine the period of rotation of the neutron star.

**Solution**

**Conceptualize**: 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 expect the star to spin faster.

**Categorize**: 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 categorize the star as an isolated system 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 expressed as \(kMR^2\), where \(k\) is some numerical constant. (From this table, for example, we see that \(k = \frac{2}{5}\) for a solid sphere and \(k = \frac{2}{3}\) for a spherical shell.)

**Analyze**

(Use the following as necessary: \(\omega\), \(T_i\), \(T_f\), \(R_f\), \(R_i\), \(k\), and \(M\).)

Let’s use the symbol \(T\) for the period, with \(T_i\) being the initial period of the star and \(T_f\) being the period of the neutron star. The star’s angular speed is given by \(\omega = \frac{2\pi}{T}\).

From the isolated system model for angular momentum, write the following equation for the star:

\[ I_i \omega_i = I_f \omega_f \]

Use \(\omega = \frac{2\pi}{T}\) to rewrite this equation in terms of the initial and final periods:

\[ I_i \left( \frac{2\pi

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