r o native the earth, that's the earth moon distance there. This is the fixed of the moon and this is its orbit velocity. Therefore we have 7.35 times ten come the twenty-two kilograms times 3.84 time ten come the eight meters squared, and also its orbital velocity is walk to it is in the one orbit i m sorry is 2 pi radians divided by its orbit period. This is the time it takes to carry out one full orbit. So the does two pi radians in every 2.36 time ten to the 6 seconds. This gives 2.89 times ten come the thirty-four kilogram meter squared every second. Now for the rotational angular momentum, we have actually the rotational minute of inertia multiply by the rotational angular velocity. Now in this instance we're modelling it as a sphere, a hard sphere, orbiting about an axis through the diameter. For this reason we have actually two times the mass of the moon multiply by the moon's radius, squared, split by five and also then multiply that by that is angular velocity that rotation which turns out to be the same as the angular velocity of its orbit because tidal results have led to the moon come rotate exactly once once it goes around the earth once, i beg your pardon is another means of saying that the exact same side of 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, divide by five, time by 2 pi radians split by 2.36 times ten come the 6 seconds. We obtain 2.37 times ten to the twenty-nine kilogram meters per second. Therefore these 2 angular momenta are different by an bespeak of magnitude, 5 orders the magnitude, ten come the thirty-four matches ten come the twenty-nine. We intended that. We intended the rotational angular momentum to be much less than the orbit angular momentum due to the fact that given the the angular velocities that rotation in orbit space the same due to the fact that they cover two pi radians in one orbit period. Then offered that those space the same, we understand that the rotational minute of inertia must be much, much much less than the moment of inertia because that the orbit due to the fact that the earth moon street is therefore much better than the radius that the moon and so this is consistent with the truth that orbit angular velocities are the same and also moment that inertia is much less in the rotation 보다 it is in the orbit. For this reason rotational angular inert is much less than the orbital angular momentum.">

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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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