Calculating Rotation Period of a Collapsing Interstellar Cloud

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SUMMARY

The discussion centers on calculating the rotation period of a collapsing interstellar cloud transitioning into a star. Given the initial parameters of mass 2.03×1030 kg and radius 1.03×1013 m, the initial rotation period is 1.43×106 years. Using the moment of inertia equations, the final rotation period of the star with a radius of 7.03×108 m is determined to be approximately 2.42 days, which is equivalent to 88.9 minutes. The calculations involve angular velocity and moment of inertia principles.

PREREQUISITES
  • Understanding of angular momentum conservation principles
  • Familiarity with moment of inertia equations
  • Knowledge of angular velocity calculations
  • Basic grasp of rotational dynamics in astrophysics
NEXT STEPS
  • Study the conservation of angular momentum in astrophysical contexts
  • Learn about the moment of inertia for different geometric shapes
  • Explore the implications of star formation on rotation periods
  • Investigate the effects of mass distribution on rotational dynamics
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Astronomy students, astrophysicists, and anyone interested in the dynamics of star formation and rotational mechanics in celestial bodies.

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Homework Statement


A uniform, spherical cloud of interstellar gas has mass 2.03×1030 kg and radius 1.03x1013m and is rotating with period 1.43×106 years. The cloud collapses to from a star 7.03x108m in radius. Find the star's rotation period.

Homework Equations


I1ω1=I2ω2
Θ=ωt

The Attempt at a Solution


Determine ω:[/B]
2π=ω(1.43×106)
ω=4.4×10-6
Use Moment of Inertia Equation: I=2/5(mr2)
I1=8.61×1055
I2=4.01×1047
∴ ω2=944.74 rad/year
Determine t:
Θ=ωt
∴ t=Θ/ω
=2π/944.74
=6.7×10-3
=2.42 days

Hey guys, I've been trying to do this homework question for a while now but I can't seem to get to the answer of 88.9 minutes. Any help getting there is much appreciated. Thank you all in advance.
 
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I agree with your method and answer.
 
Wow odd. I will ask the teacher about the provided answer being incorrect then, thank you for shedding some light on this haruspex.
 

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