Serway & Jewett — Universal Gravitation: Problem 26

After reading Sections 13.2 and 13.3, your classmate looks online to gather information about neutron stars. He finds that a typical radius of a neutron star is 10 km, a typical mass is two solar masses, and that a typical rotation period is as short as 1.4 ms. He suggests that if a spherical neutron star were spinning that fast, it seems that material at the equator of the sphere would be flung away because the gravity of the star could not supply the needed centripetal acceleration of the material. Prepare an argument that shows that the gravity at the surface of a neutron star is more than sufficient to provide the centripetal acceleration. (Note: Neutron stars typically have the same mass as our Sun.)