Calculate the moment of inertia of the earth about its diameter, taking it to be a sphere of 10^25kg and diameter 12800 km?
Answer: 1.64 × 10^38kgm^3
Explanation
To calculate the moment of inertia of the Earth about its diameter, we can use the formula for the moment of inertia of a sphere:
I = (2/5)MR^2
where:
I = moment of inertia
M = mass of the Earth (10^25 kg)
R = radius of the Earth (diameter/2 = 12800 km / 2 = 6400 km = 6.4 × 10^6 m)
Plugging in the values, we get:
I = (2/5) × 10^25 kg × (6.4 × 10^6 m)^2
= (2/5) × 10^25 kg × 4.096 × 10^13 m^2
= 1.6384 × 10^38 kg m^2
≈ 1.64 × 10^38 kg m^2
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