The sun turns on its axis once every 26.0 days. Its mass is 2.0x10 30 kg and its

Question

The sun turns on its axis once every 26.0 days. Its mass is 2.0x1030 kg and its radius is 7.0x108 m. Assume it is a rigid sphere of uniform density.
(a) What is the sun’s angular momentum?
In a few billion years, astrophysicists predict that the sun will use up all its sources of nuclear energy, and will collapse into a ball of exotic, dense matter known as a white dwarf. Assume that its radius becomes 5.8 ? 106 m (similar to the size of the Earth.) Assume it does not lose any mass between now and then.
(b) What will be its angular speed if its angular momentum is conserved?
(c) How long will it take to turn once on its axis?

Explanation / Answer

a)

T = time period = 26 days = 24 x 3600 x 26 sec = 2.25 x 106 sec

wi = angular velocity = 2pi/T = 2 x 3.14/(2.25 x 106 ) = 2.8 x 10-6 rad/s

Ii = moment of inertia = (0.4) M R2 = (0.4) (2 x 1030) (7 x 108)2 = 3.92 x 1047 kgm2

angular momentum is given as

Li = Ii wi = (3.92 x 1047) (2.8 x 10-6) = 1.1 x 1042

b)

If = moment of inertia = (0.4) M R2 = (0.4) (2 x 1030) (5.8 x 106)2 = 2.7 x 1043 kgm2

wf = ?

using conservation of momentum

Li = If wf

1.1 x 1042 = (2.7 x 1043) wf

wf = 0.041 rad/s

c)

wf = 0.041 = 2pi/T

T = 0.041/(6.28) = 0.0065 sec

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.