Would you imagine that the moment of inertia of the earth around its own axis is a negligible fraction of its moment of inertia about the axis of rotation around the sun. Support your explanation with substantial data.
Answers
Yes, the moment of inertia of the earth around its own axis is a negligible fraction of its moment of inertia about the axis of rotation around the sun.
Moment of inertia of the earth around its own axis:
Moment of inertia of sphere around its centre is given by the formula:
I = mr²/5
Where,
m = Mass of the sphere (mass of the earth = 6 × 10²⁴ kg)
r = Radius of the sphere (radius of the earth = 6.3 × 10⁹ m)
Now, the moment of inertia of earth is:
I₁ = ((6 × 10²⁴) × (6.3 × 10⁹)²)/5
∴ I₁ = 7.56 × 10³⁶ kg/m²
Moment of inertia about the axis of rotation around the sun:
Moment of inertia of sphere around axis of rotation is given by the formula:
I = mr²
Where,
m = Mass of the sphere (mass of the earth = 6 × 10²⁴ kg)
r = Radius of the sphere (radius of the earth rotation = 1.5 × 10¹¹ m)
Now, the moment of inertia of earth is:
I₂ = 6 × 10²⁴ × (1.5 × 10¹¹)²
∴ I₂ = 9 × 10⁴⁶ kg/m²
Thus, moment of inertia of sphere around its centre is a negligible fraction of moment of inertia of sphere around axis of rotation.
7.56 × 10³⁶ kg/m² is negligible compared to 9 × 10⁴⁶ kg/m²