Occasionally, a rotating neutron star undergoes a sudden andunexpected speedup c

Question

Occasionally, a rotating neutron star undergoes a sudden andunexpected speedup called a glitch. One explanation isthat a glitch occurs when the crust of the neutron star settlesslightly, decreasing the moment of inertia about the rotation axis.Suppose a neutron star with angular speed0 = 70.5 rad/sunderwent such a glitch that increased its angular speed to = 0 +, where/0 = 2.02 x 10-6. If the radius ofthe neutron star before the glitch was 10.8 km, by how much did its radius decrease in thestarquake? Assume that the neutron star is a uniform sphere

Explanation / Answer

According to conservation of angular momentum we have            Li =Lf ==> Ioo = Iff ==> (2/5)MRo2o2 =(2/5)MRf2 [o+]2 ==> Rf2 = Ro2 / ( 1 +/o)               = (10.8 km)2 / ( 1 + 2.02 x 10-6)               = 116.63 km2 ==> Rf = 10.79 km Therefore the radius decreased to 10.8 km-10.79 km = 0.01 km

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