The Earth has mass ME and average radius RE. The Moon has mass MM and the average distance from the center of mass of the moon to the center of mass of the Earth is DM. For this problem use the following constants.

Mass of the Earth: 5.97E24 kgMass of the Moon: 7.35E22 kgRadius of the Earth: 6,371 km
Find an expression for the moment of inertia IEof the Earth on its axis in terms of the given parameters.

The moment of inertia of Earth   = = 9.7  10^37 kg m^2

Find an expression for the moment of inertia

The Moment of Inertia  of solid sphere about the axis passing through center of mass of is defined by equation (1) as

........ (1)

According to the given question

Moment of Inertia of Earth =

Mass of Earth =

Radius of the Earth =

Considering Earth to be a Solid sphere

Putting these variables in equation (1) we get the expression

According to the given data

Mass of Earth= 5.97 kg

= Radius of Earth = 6,371 km= 6371000 m

Hence

The moment of Inertia of earth   = = (2/5) 5.97 kg  6371000 m  6371000 m = 9.7  10^37 kg m^2

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Moment of inertia of Earth about its own axis is given as

Explanation:

Since Earth is considered as solid sphere

So we will have

so we will have

so we have

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