Question

1) Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 14.0 km. Determine the greatest possible angular speed the neutron star can have so that the matter at its surface on the equator is just held in orbit by the gravitational force. (The mass of the Sun is 1.99 1030 kg.)

______________________rad/s

Answer 1

$\small F=\frac{Gm_1m_2}{r^2}$ , Newton's law of universal graviation

$\small F=ma$ , Newton's second law

$\small \frac{F}{m}=a=g=\frac{GM_{star}}{(r_{star})^2}=\frac{6.67x10^{-11}(2)(1.99x10^{30})}{(14x10^3)^2}$

$\small g=1.35x10^{12} m/s^2$

$\small a_N=\frac{v^2}{r}=\frac{ \omega^2 r^2}{r}=\omega^2r$ , the normal (or centripetal) acceleration will be equatl to the force of gravity, so

$\small \sqrt{\frac{g}{r}}=\sqrt{\frac{1.35x10^{12}}{14x10^3}}=\omega$

$\small \omega= 9819.81 rad/s$