Question

Suppose a star with the Sun’s mass and radius (the radius of the
Sun is 6.96×10^{8} m) is rotating with a period of 25 days.
The star first blows off its outer layers and loses mass and
angular momentum before the actual collapse, thereby reducing its
radius while maintaining the same density. Then, with a mass that
is 59 % of the Sun’s mass, it collapses to a white dwarf with a
rotation period is 131 s.

A) What is the radius of this white dwarf?

B) Compare your answer with the radius of Earth.

C) Compare your answer with the radius of the Sun.

Answer #1

Here we apply concept of conservation of angular momentum.

In a little over 5 billion years, our Sun will collapse to a
white dwarf approximately 16,000 km in diameter. (Ignore the fact
that the Sun will lose mass as it ages.) (a) What will our Sun’s
angular momentum and rotation rate be as a white dwarf? (Express
your answers as multiples of its present-day values.) (b) Compared
to its present value, will the Sun’s rotational kinetic energy
increase, decrease, or stay the same when it becomes a white dwarf?...

Suppose a star the size of our Sun, but of mass 8.0 times as
great, was rotating at a speed of 1.0 revolution every 21 days. If
it were to undergo gravitational collapse to a neutron star of
radius 20 km, losing three quarters of its mass in the process,
what would its rotation speed be? Assume that the star is a uniform
sphere at all times and that the lost mass carries off no angular
momentum.
Answer in rev/day

Suppose a star the size of our Sun, but with mass 5.0 times as
great, were rotating at a speed of 1.0 revolution every 15 days. If
it were to undergo gravitational collapse to a neutron star of
radius 14 km , losing three-quarters of its mass in the process,
what would its rotation speed be? Assume also that the thrown- off
mass carries off either
Part A) No angular momentum
Part B) its proportional share three-quarters of the initial...

Suppose a star the size of our Sun, but with mass 8.0 times as
great, were rotating at a speed of 1.0 revolution every 8.0 days.
If it were to undergo gravitational collapse to a neutron star of
radius 11 km , losing three-quarters of its mass in the process,
what would its rotation speed be? Assume also that the thrown- off
mass carries off either
a) no angular momentum
b)its proportional share three-quarters of the initial angular
momentum
Express...

Suppose a star the size of our Sun
(r=7.0*105 km), but with mass
6.0 times as great, were rotating at a speed of 1.0 revolution
every 10 days. If it were to undergo gravitational collapse to a
neutron star of radius 10 km, losing 2/3 of its mass in the
process, what would its rotation period be in
μs? Assume the star is a uniform sphere
at all times. Assume also that the thrown-off mass carries off no
angular momentum....

Suppose a star of mass M at the end of its evolution collapses
into a white dwarf, losing half its mass. In the cataclysmic end
process the mass thrown off carries no angular momentum, but the
core collapses to 1.0% of the original size of the star.
a. If the original star rotated at a rate of once per 30 days,
what would its new rotation rate be?
b.
What would be the ratio of its final rotational kinetic energy...

A uniform, spherical cloud of interstellar gas has mass 1.8×1030
kg and radius 1.0×1013 m , and is rotating with period 1.3×106
years. If the cloud collapses to form a star 6.8×108 m in radius,
what will be the star's rotation period?

a) In a little over 5 billion years, our star will slough off
~20% of its mass and collapse to a white dwarf star of radius 8,000
km. We will model it as a sphere. What will its angular momentum be
in terms of its current angular momentum? What will its rotation
period be in terms of its current period?
b) (12 points) What will its rotational kinetic energy be in
terms of its current rotational kinetic energy?

Astronomers detect stars that are rotating extremely rapidly,
known as neutron stars. A neutron star is believed to form from the
inner core of a larder star that collapsed, under its own
gravitation, to a star of very small radius and very high density.
Before collapse, suppose the ore of such a star is the size of our
Sun (R = 7105km)with mass 2.0 times as great as the Sun, and is
rotating at a frequency of 1.0 revolution every...

Suppose our Sun eventually collapses into a white dwarf, in the
process losing about two thirds of its mass and winding up with a
radius 2.0 percent of its existing radius. What would its new
rotation rate be? (Take the Sun's current period to be about 30
days.)
____ rad/s
What would be its final KE in terms of its initial KE of
today?
(KEfinal / KEinitial) = ____

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