At the end of its life (in about 5 billion years, when it has used up all ts fue
ID: 2032532 • Letter: A
Question
At the end of its life (in about 5 billion years, when it has used up all ts fuel), the sun will expand into a red giant (and swallow he earth) and then explode as a supernova. At the end of this process, a small and very dense remnant called a white dwarf will remain. A typical white dwarf produced by a star like our sun has about half the original mass of the star, but a radius that is a 100 times smaller. Consider a model of supernova explosion in which the sun is a uniform sphere, and so is the white dwarf. All the matter in the sun at r 2R/ rotational period is about 30 days (different parts of the sun rotate at different rates - this is an approximate average). How much rotational kinetic energy does it have now, and how much willthe white dwarf have (according to this model)?Explanation / Answer
Moment of inertia = 2/5 MR^2
where M = mass ,R = radius
MOI = 2/5 * 2*10^30 * (7*10^8)^2
= 3.92*10^47 kg-m^2
RotationalKE = 0.5Iw^2
= 0.5*(3.92*10^47)*(2pi/30*24*60*60)^2
= 1.15*10^36 J
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