Question

Learning Goal: To understand the concept of moment of inertia and how it depends on mass, radius, and mass distribution.

Answer 1

Answer:

 m₂ = 4 kg

Explanation:

The moment of inertia is defined by

         I = ∫ r² dm

for bodies with high symmetry it is tabulated, for a spherical shell

        I = 2/3 m r²

in this case the first sphere has a radius of r₁ = 2m and a mass of m₁ = 1 kg, the second sphere has a radius r₂ = 1m.

They ask what is the masses of the second spherical shell so that the moment of inertia of the two is the same.

        I₁ = ⅔ m₁ r₁²

        I₂ = ⅔ m₂ r₂²

They ask that the two moments have been equal

        I₁ = I₂

        ⅔ m₁ r₁² = ⅔ m₂ r₂²

         m₂ = (r₁ / r₂) ² m₁

let's calculate

         m₂ = (2/1) ² 1

         m₂ = 4 kg