Acompound disk of outside diameter 128 cm is made up of a uniform solid disk of radius 37.0 cm and area density 4.60 g/cm2 surrounded by a concentric ring of inner radius 37.0 cm, outer radius 64.0 cm, and area density 1.60 g/cm2find the moment of inertia of this object about an axis perpendicular to the plane of the object and passing through its center. in kg/m^2.

I total = 5,101 kg m²

Explanation:

The moment of inertia of a body is given by the expression

     I = ∫ r² dm

For some bodies with symmetry they are tabulated, for an axis that passes through its center

Disc                I = ½ M R2

hollow ring    I = ½ M (R12 + R22)

let's apply this equation our case.

The body is formed by two consecutive bodies a disc plus a hollow ring, with the same center of rotation, so the moment of inertia that is a scalar we can add

      I total = I disk + I ring

To find the mass let's use the definition of density

       ρ = m / A

The area of a circle is

        A = π R²

Disk

        A₁ = π 37²

        A₁ = 4.30 10³ cm2

Ring

       A₂ = π (R₂² - r₁²)

       A₂ = π (64² - 37²)

       A₂ = 8.57 10³ cm2

We cleared the dough

       m = ρ A

Disk

       m₁ = 4.60 4.30 10³

       m₁ = 19.78 10³ g = 19.78 kg

Ring

      m₂ = ρ₂ A₂

      m₂ = 1.60 8.57 10³

      m₂ = 13,712 10³ g = 13,712 kg

Now we can calculate the moments of inertia of each body

     I disk = ½ 19.78 0.37²

     I disk = 1,354 kg m²

     I ring = = ½ 13,712 (0.37² + 0.64²)

     I ring = 3.747 Kg m²

The moment of total inertia

     I total = I disk + I ring

     I total = 1,354 + 3,747

     I total = 5,101 kg m²

Note that the total radius of the system is 101 cm

an energy transformation flow diagram is shown

where is it ?

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.