heastonk9136
18.09.2019 •
Mathematics
Two spherical shells have their mass uniformly distrubuted over the spherical surface. one of the shells has a diameter of 2 meters and a mass of 1 kilogram. the other shell has a diameter of 1 meter. what must the mass m of the 1-meter shell be for both shells to have the same moment of inertia about their centers of mass?
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Ответ:
If two spheres have the same moment of inertia, then
I₁ = I₂
m₁(r₁)² = m₂(r₂)²
Solve for the second mass:
m₂ = m₁ (r₁/r₂)²
Given m₁ = 1 kg, r₁ = 2 m, r₂ = 1m,
m₂ = (1 kg) (2 m / 1 m)² = 4 kg
Ответ: