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scoldham

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Hi, Long time pf reader... first time poster in need of physics help.

The moment of inertia of the Earth is approximately 0.331M

[tex]\omega[/tex]

Sub A is for Asteriod

Sub E is for Earth

Sub sys is for system (Asteroid + Earth)

I

Note: V

I

So essentially, I derived the equations above based on conservation of angular momentum. I assume the point of the line in the problem statement about 45 degrees striking along the equatorial plane is telling me the asteroid's momentum is exactly converse the Earth's ergo 1 dimension.

After calculating I

I would think that even though the asteroid is 6 times smaller than the Earth, it would make more of a difference than that... am I right? Guidance much appreciated.

## Homework Statement

The moment of inertia of the Earth is approximately 0.331M

_{E}R_{E}^{2}. If an asteroid of mass 5.0 × 10^{18}kg moving at 150 km/s struck (and stuck in) the Earth’s surface, by how long would the length of the day change? Assume the steroid was traveling westward in the equatorial plane and struck the Earth’s surface at 45◦.[tex]\omega[/tex]

_{E}= 1/86400 rev/secSub A is for Asteriod

Sub E is for Earth

Sub sys is for system (Asteroid + Earth)

## Homework Equations

I

_{sys}[tex]\omega[/tex]_{sys}= I_{E}[tex]\omega[/tex]_{E}+ V_{A}Note: V

_{A}= R_{A}[tex]\omega[/tex]_{A}I

_{sys}= (0.311*M_{E}-M_{A}) R_{E}^{2}## The Attempt at a Solution

So essentially, I derived the equations above based on conservation of angular momentum. I assume the point of the line in the problem statement about 45 degrees striking along the equatorial plane is telling me the asteroid's momentum is exactly converse the Earth's ergo 1 dimension.

After calculating I

_{sys}, I solved the first equation for [tex]\omega[/tex]_{sys}and then plugged in the given data... I'm getting 1.16 * 10^{-5}for [tex]\omega[/tex]_{E}implying (to me at least) that the change in the length of a day is less than 100 seconds if that...I would think that even though the asteroid is 6 times smaller than the Earth, it would make more of a difference than that... am I right? Guidance much appreciated.

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