You are watching: What is the angular momentum of the moon around the earth?
This is college Physics Answers through Shaun Dychko. The orbital momentum of the moon is the orbital minute of inertia multiplied by the orbit angular velocity. We can model it as a single point fixed a distance r o from the earth, that"s the planet moon street there. This is the mass of the moon and this is its orbit velocity. So we have actually 7.35 times ten to the twenty-two kilograms times 3.84 times ten come the eight meter squared, and also its orbit velocity is walk to it is in the one orbit i beg your pardon is two pi radians divided by its orbit period. This is the moment it takes to carry out one full orbit. So that does 2 pi radians in every 2.36 time ten come the 6 seconds. This provides 2.89 times ten to the thirty-four kilogram meter squared per second. Now for the rotational angular momentum, we have actually the rotational minute of inertia multiplied by the rotational angular velocity. Currently in this instance we"re modelling it together a sphere, a heavy sphere, orbiting around an axis with the diameter. Therefore we have actually two time the fixed of the moon multiply by the moon"s radius, squared, split by five and then multiply that by that angular velocity that rotation which transforms out to be the very same as the angular velocity of its orbit since tidal effects have resulted in the moon come rotate specifically once when it goes roughly the planet once, i m sorry is another means of saying the the same side the the moon is always facing the earth. So, we have actually two times the mass multiplied by the radius the the moon, 1.74 time ten to the 6 meters, square that, division by five, time by two pi radians divided by 2.36 time ten to the six seconds. We obtain 2.37 times ten to the twenty-nine kilogram meters every second. Therefore these 2 angular momenta are various by an stimulate of magnitude, 5 orders the magnitude, ten come the thirty-four versus ten come the twenty-nine. We expected that. We supposed the rotational angular inert to be much less than the orbital angular momentum due to the fact that given the the angular velocities of rotation in orbit space the same because they cover two pi radians in one orbit period. Then offered that those are the same, we recognize that the rotational minute of inertia have to be much, much less than the minute of inertia for the orbit because the earth moon street is for this reason much greater than the radius of the moon and so this is continual with the reality that orbit angular velocities space the same and moment of inertia is much less in the rotation than it is in the orbit. Therefore rotational angular momentum is less than the orbit angular momentum.
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