Under some circumstances, a star can collapse into an extremely dense object mad
ID: 2214233 • Letter: U
Question
Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was 8.0105 (comparable to our sun); its final radius is 16 .a)If the original star rotated once in 32 days, find the angular speed of the neutron star.
Express your answer using two significant figures.
Explanation / Answer
Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 10^14 times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was 6.0×10^5 (comparable to our sun); its final radius is 18 km . This is probably an exercise in conservation of angular momentum with classical mechanics intended to be applied. Simply require that angular momentum before (=Lb) equal angular momentum after (=La). Let the angular rotational rates before and after be Ab and Aa respectively. Likewise for the radii, let's use Rb and Ra. Then: Lb = k*(Rb^2)*Ab = La = k*(Ra^2)*Aa. The constant k doesn't matter here for our purposes. We see the quantity to be conserved is actually R^2*A. Solve for Aa: Aa = Ab*(Rb/Ra)^2. Now just plug in the values!! I get Ab = 2*pi radians/ 35 days = 2.08*10^-6 rad/sec. so that Aa = (2.08*10^-6rad/s)*(6*10^5km/18km)^2 = 2,310 rad/sec.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.