Given the following information, what would the star's rotation speed be?

Question

Suppose a star the size of our Sun, but with mass 3.0 times as great, were rotating at a speed of 1.0 revolution every 11 days. If it were to undergo gravitational collapse to a neutron star of radius 15 km, losing three-quarters of its mass in the process, what would its rotation speed be

Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.

Olivia Aldridge · Accepted Answer

#I_1\omega_1 = I_2\omega_2 \qquad => \omega_2 = (I_1/I_2)\omega_1 #
#\qquad \quad \omega_2= (8.6118 imes10^9) imes(6.611 imes10^{-6}) = 5.693 imes10^{4} (rad)/s# Angular Momentum Conservation: A system's net angular momentum is conserved in the absence of an external torque. #L = I\omega = const \qquad => I_1\omega_1 = I_2\omega_2# #I_1, I_2# - Moment of inertia before and after collapse. #\omega_1, \omega_2# - Angular speed before and after collapse. #T_1, T_2# - Rotational time period before and after collapse. The Moment-of-Inertia of a sphere of mass #M# and radius #R# spinning along an axis passing through its centre is : #I=2/5MR^2# #I_1/I_2 = (2/5 M_1R_1^2) / (2/5 M_2R_2^2) = (M_1/M_2)(R_1/R_2)^2# # \qquad = 4((6.96 imes10^5\quad km)/(15 \quad km))^2 = 8.6118 imes10^9# #M_1 = M_{sun}; \qquad M_2 = M_{sun}/4; \qquad # #R_1 = R_{sun} = 6.96 imes10^5\quad km; \qquad R_2 = 15\quad km;# #\omega_1 = (2\pi)/T_1 = (2\pi)/(11 \quad days)= ((2\pi)/(11 imes24 imes3600\quad s))# #\qquad =6.611 imes10^{-6}\quad rad.s^{-1}# #I_1\omega_1 = I_2\omega_2 \qquad => \omega_2 = (I_1/I_2)\omega_1 # #\qquad \quad \omega_2= (8.6118 imes10^9) imes(6.611 imes10^{-6}) = 5.693 imes10^{4} (rad)/s# #T_2 = (2\pi)/omega_2 = 0.11 imes10^{-3} \quad s = 0.11 \quad milli-seconds# A Pulsar with milliseconds?

Clara Avalos · Answer

undefined To determine the rotation speed of a star, we need specific information such as its radius, mass, and rotational period. Without these details, it's not possible to calculate the rotation speed accurately.