- #1

toesockshoe

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## Homework Statement

Given that we know the mass of the moon and the Earth and the distance between their centers as the moon orbits the earth, if the Earth's angular velocity about its own axis is slowing down from say some initial given omega to a final omega (due to tidal friction in reality), find out what happens to the orbital distance between the Earth and moon as a consequence

## Homework Equations

[itex] F_g = \frac{Gm_mm_E}{r^2} [/itex][/B]

## The Attempt at a Solution

My first guess is that this is an angular momentum conservation problem becuase if you make the origin the center of the earth, there are no net external torques.

soo...

[itex] L_i = L_f [/itex]

[itex] r_{imoon} x p_i + I_{earth} \omega _i = r_{fmoon} x p_f + I_{earth} \omega _f [/itex]

[itex] r_im_m \frac {v_{imoon}}{r_i} + I\omega_i = r_fm_m \frac{v_{fmoon}}{r_f} + I\omega_f [/itex]

obviously this is wrong, as the r's cancel out and we arent left with the variable we are trying to solve. How would I go about solving this problem and where am I going wrong?[/B]