Meteorite strikes Earth; Change in rotational frequency

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Homework Statement



Suppose a 5.7×10^10 kg meteorite struck the Earth at the equator with a speed 3.0×10^4 m/s, making a 45 degree angle (see figure) and remained stuck.By what factor would this affect the rotational frequency of the Earth (1rev/day)?

GIANCOLI.ch11.p49.jpg



Homework Equations



It seems like an inelastic collision and I suppose that the following equation will also be used:

w_f = v/R

(w_f - w_i)/w_i


The Attempt at a Solution



I figured out the initial angular velocity of Earth but don't know what the final angular velocity will be because I don't think it will be as easy as plugging in numbers on w_f= v/R. The mass of the meteorite must be considered at some point, right?

w_E = (1rev/day)(2pi/1 rev)(1 day/24hr)(1hr/3600s)=7.27^-5 rad/s

 
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Is it angular momentum (L)?

L = Iw

So, I_i x w_i = I_f x w_f

where I_i = 2/5 (M_E)(r_E)^2

and I_f = I_i + I of meteor, but I don't know the radius of the meteor...

If I did, I guess I could solve for w_f and take it from there.
 
So maybe the relevant equation is L = Rmv?

The initial angular momentum would be: L = Iw_i = [(2/5)MR^2]w_i

where M = mass of Earth

and L_m (for meteor) = rmv, where m= mass of meteor?
 
If my previous thread is correct, how do I get w_f ?
 
Angular momentum is the correct conserved quantity. That means that the total angular momentum just after the collision is equal to the total angular momentum just prior to the collision. Prior to the collision you have two objects, one translating and the other rotating. After the collision all you have is one rotating object.

Is the meteor going to change the Earth's moment of inertia by any significant amount?
 
NOt sure... Still don't know how to set it up.
 
Thanks for the help but I found another post on another website that took me through the whole process which is what I needed to see how it was done instead of guessing randomly.

THanks anyway