Calculating Rotation Period of a Collapsing Interstellar Cloud

[gex]

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.

 

[haruspex]

I agree with your method and answer.

 

[gex]

Wow odd. I will ask the teacher about the provided answer being incorrect then, thank you for shedding some light on this haruspex.