During most of its lifetime, a star maintains an equilibriumsize in which the in

Question

During most of its lifetime, a star maintains an equilibriumsize in which the inward force of gravity on each atom is balancedby an outward pressure force due to the heat of the nuclearreactions in the core. But after all the hydrogen "fuel" isconsumed by nuclear fusion, the pressure force drops and the starundergoes a gravitational collapse until it becomes aneutron star. In a neutron star, the electrons and protonsof the atoms are squeezed together by gravity until they fuse intoneutrons. Neutron stars spin very rapidly and emit intense pulsesof radio and light waves, one pulse per rotation. These "pulsingstars" were discovered in the 1960s and are calledpulsars. 1.A star with the mass (M= 2.0 x 10^30) and size (R= 3.5 x10^8) of our sun rotates once every 35.0 days. After undergoinggravitational collapse, the star forms a pulsar that is observed byastronomers to emit radio pulses every 0.200s. By treating theneutron star as a solid sphere, deduce its radius. 2.What is the speed of a point on the equator of the neutronstar? Your answer will be somewhat too large because a star cannotbe accurately modeled as a solid sphere. During most of its lifetime, a star maintains an equilibriumsize in which the inward force of gravity on each atom is balancedby an outward pressure force due to the heat of the nuclearreactions in the core. But after all the hydrogen "fuel" isconsumed by nuclear fusion, the pressure force drops and the starundergoes a gravitational collapse until it becomes aneutron star. In a neutron star, the electrons and protonsof the atoms are squeezed together by gravity until they fuse intoneutrons. Neutron stars spin very rapidly and emit intense pulsesof radio and light waves, one pulse per rotation. These "pulsingstars" were discovered in the 1960s and are calledpulsars. 1.A star with the mass (M= 2.0 x 10^30) and size (R= 3.5 x10^8) of our sun rotates once every 35.0 days. After undergoinggravitational collapse, the star forms a pulsar that is observed byastronomers to emit radio pulses every 0.200s. By treating theneutron star as a solid sphere, deduce its radius. 2.What is the speed of a point on the equator of the neutronstar? Your answer will be somewhat too large because a star cannotbe accurately modeled as a solid sphere.

Explanation / Answer

Part A . initial ang mom = final ang mom .     mom of inertia * ang speed = mom of inertia * ang speed .       (2/5) m R2 * 2 / T    =     (2/5)m r2 * 2 / t .          R2 t / T   = r2 .    r = 3.5 x 108 * (0.200 /35*86400)1/2 = 90010.3 meters = 90km   is the radius . Part B .         speed = distance /time = 2r / t = 2 * 90010.3 /0.200 = 2.83*106 m/s .    r = 3.5 x 108 * (0.200 /35*86400)1/2 = 90010.3 meters = 90km   is the radius . Part B .         speed = distance /time = 2r / t = 2 * 90010.3 /0.200 = 2.83*106 m/s

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