A 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 star undergoes a supernova explosion, the stellar core, which had a radius of 1.1 x 10“ 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 v 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 KMR2, where k is some numerical constant. (From this table, for example, we see that k = for a solid sphere and k = 2 for a spherical shell.)

A 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 star undergoes a supernova explosion, the stellar core, which had a radius of 1.1 x 10“ 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 v 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 KMR2, where k is some numerical constant. (From this table, for example, we see that k = for a solid sphere and k = 2 for a spherical shell.)