The moment of inertia of a solid sphere with uniform density is given by:
I = (2/5) * M * R^2
Where M is the mass of the sphere and R is its radius. Plugging in the given values:
I = (2/5) * (5.98 × 10^24 kg) * (6370 km)^2
I = 9.98 × 10^37 kg * m^2
The kinetic energy of rotation can be calculated using the formula:
KE = (1/2) * I * ω^2
Where ω is the angular velocity of rotation. We don't know the exact value of ω for the Earth, but we can estimate it as 2π/24 hr, since the Earth rotates once every 24 hours. Converting this to radians per second:
ω = 2π / (24 * 60 * 60 s) = 7.27 × 10^-5 rad/s
Plugging in the values:
KE = (1/2) * (9.98 × 10^37 kg * m^2) * (7.27 × 10^-5 rad/s)^2
KE = 2.14 × 10^29 J
Therefore, the moment of inertia of the Earth with respect to rotation about its axis is 9.98 × 10^37 kg * m^2, and the kinetic energy of this rotation is 2.14 × 10^29 J.
Assume that the Earth is a solid sphere of constant density, with mass 5.98 × 1024 kg and radius 6370 km.
What is the moment of inertia of the Earth with respect to rotation about its axis, and what is the kinetic energy of this rotation?
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