Calculate the moment of inertia of the earth about its axis of rotation. Mass of the earth is 5.91 ×10^24 kg and its radius is 6.38×10^6 m. The moment of a solid sphere about its axis of rotation is I=2/5 M R²
Question
Calculate the moment of inertia of the earth about its axis of rotation. Mass of the earth is 5.91 ×10^24 kg and its radius is 6.38×10^6 m. The moment of a solid sphere about its axis of rotation is I=2/5 M R²
Solution
To calculate the moment of inertia of the Earth about its axis of rotation, we can use the formula for the moment of inertia of a solid sphere, which is given as I = 2/5 M R².
Here, M is the mass of the Earth and R is the radius of the Earth.
Given: M = 5.91 ×10^24 kg (mass of the Earth) R = 6.38×10^6 m (radius of the Earth)
Substituting these values into the formula, we get:
I = 2/5 * (5.91 ×10^24 kg) * (6.38×10^6 m)²
Now, we just need to calculate the value.
I = 0.4 * 5.91 ×10^24 kg * 4.07x10^13 m²
I = 2.364 * 10^24 kg * 4.07x10^13 m²
I = 9.62 * 10^37 kg.m²
So, the moment of inertia of the Earth about its axis of rotation is approximately 9.62 * 10^37 kg.m².
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