Concept explainers
The rotational inertia of the Earth-Moon system around its center of mass.
Answer to Problem 60PQ
The rotational inertia of the Earth-Moon system around its center of mass is
Explanation of Solution
Assume that origin is at the Earth’s center.
Write the expression for the center of mass of a system.
Here,
The system consists of the Earth and the Moon.
Since the origin is taken at the center of the Earth, value of
Expand equation (I) for the Earth-Moon system.
Here,
The mass of the Earth is
Substitute
The value of
Write the equation for the rotational inertia of the Moon around the center of mass of the system.
Here,
Write the equation for
Put the above equation in equation (II).
The Earth can be modelled as a solid sphere rotating around a point somewhat offset from its own center of mass so that parallel axis theorem can be used to find the rotational inertia of the Earth.
Here,
Write the equation for
Here,
Since the center of the Earth is the origin, the perpendicular distance between the center of mass of the system and the center of the Earth will be equal to the position of the center of mass of the system.
Put the above two equations in equation (IV).
Write the equation for the rotational inertia of the Earth-Moon system around the center of mass of the system.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the rotational inertia of the Earth-Moon system around its center of mass is
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Chapter 13 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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