Under some circumstances, an ordinary star can collapse into an extremely dense
ID: 1373630 • Letter: U
Question
Under some circumstances, an ordinary star can collapse into an extremely dense object made mostly of neutrons. This type of star is called a "neutron star". A neutron star has a mass density roughly 1014 times larger than that of ordinary solid matter.
Suppose we represent an ordinary star as a uniform solid rigid sphere, both before and after the collapse. The original star's initial radius is 7.0 x 105 km (comparable to the size of our sun). After it collapses, its final radius is only 16 km! If the original star makes one complete rotation about its axis once per month (every 30 days), find the neutron star's period of rotation just after the original star has collapsed.
New period:
Explanation / Answer
Since angular momentum of the system is conserved
I1*w1 = I2*w2
m*R1^2*w1 = m*R2^2*w2
new angular speed is w2 = w1*(R1/R2)^2 = (2*pi/(30*24*60*60))*(7*10^5/16)^2 = 4639.8 rad/sec
new time period is T2 = 2*pi/w2 =(2*3.142)/(4639.8) = 0.001354 sec
T2 = 0.001354/(24*60*60) = 1.56*10^-8 days
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