Meteorite strikes Earth; Change in rotational frequency

[pcml100]

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)?

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

 

[D H]

A certain conservation principle applies here. What is it?

 

[pcml100]

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.

 

[D H]

Do you think the rotational angular momentum is going to account for much?

Angular momentum also results from translational motion. What are the relevant equations here?

 

[pcml100]

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?

 

[pcml100]

If my previous thread is correct, how do I get w_f ?

 

[D H]

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?

 

[pcml100]

NOt sure... Still don't know how to set it up.

 

[D H]

What is the total angular momentum before the collision? What is the angular momentum after the collision?

 

[pcml100]

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

 

[D H]

I didn't want you to guess. I wanted you to reason things out rationally. When you are confronted with some difficult problem in real life you will not always have websites around as a crutch. Learning how to think is the most important thing you can learn in school.