The Question reads: A neutron star forms when a star larger than our Suncollapse

Question

1. A neutron star forms when a star larger than our Suncollapses to form a much more compact star through gravitationalcollapse. Suppose the original star has a period of rotationof 25 days (25 days = 2.16x106 seconds) similar to ourSun but has a radius of 2x109m. What is the periodof rotation if the neutron star has the same mass as the originalstar but the radius of the neutron star is reduced to2x105 m? Period of rotation is _______seconds.(work using conservation of angular momentum and relationshipbetween T and w. Assume the star is a uniform sphere, I =2/5MR2,with Ri and Rf )

1. A neutron star forms when a star larger than our Suncollapses to form a much more compact star through gravitationalcollapse. Suppose the original star has a period of rotationof 25 days (25 days = 2.16x106 seconds) similar to ourSun but has a radius of 2x109m. What is the periodof rotation if the neutron star has the same mass as the originalstar but the radius of the neutron star is reduced to2x105 m? Period of rotation is _______seconds.(work using conservation of angular momentum and relationshipbetween T and w. Assume the star is a uniform sphere, I =2/5MR2,with Ri and Rf )

Explanation / Answer

    Initial time-period, T1 = 25 days = 2.16 X 106 s    Initial radius, R1 = 2 X 10 9 m     New time-period, T2 = ?     New radius , R2 = 2 X 10 5 m     From law of conservation of angularmomentum,     I1 1 = I2 2     ( 2/5 ) ( M R1 2 ) ( 2 / T1 ) = ( 2/5 ) ( M R2 2 ) ( 2 / T2 )                     R1 2 / T1 = R2 2 / T2                            T2 = ( R2 / R1 ) 2 * T1                                 = ( 2 X 10 5 / 2 X 10 9 ) 2 * 2.16X 10 6                                            = 2.16 X 10 -2 s

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