Question

In the following problems, assume the following parameters:

Answer 1

Answer:

1) a)  I₁ = 0.2941 kg m², b)  I₂ = 0.2963 kg m², c) I_{total} = 0.5904 kg m²

3)   α = 6.31 10⁶ rad / s²

Explanation:

1) The moment of inertia for bodies with high symmetry is tabulated, for a divo with an axis passing through its center is

         I = ½ m r²

a) moment of inertia of the upper disk

        I₁ = ½ m₁ r₁²

        I₁ = ½ 1,468 0.633²

        I₁ = 0.2941 kg m²

b) upper aluminum disc moment of inertia

        I₂ = ½ m₂ r₂²

        I₂ = ½ 1.479 0.633²

        I₂ = 0.2963 kg m²

c) the moment of inertia is an additive scalar quantity therefore

         I_{total} = I₁ + I₂

         I_{total} = 0.2941 + 0.2963

         I_{total} = 0.5904 kg m²

3) ask the value of the angular acceleration, that is, the second derivative of the angle with respect to time squared

indicate the angular velocity of the system w = 400 rev / s

Let's reduce the SI system

        w = 400 rev / s (2π rad / rev) = 2513.27 rad / s

as the system is rotating we can calculate the centripetal acceleration

          a = w² R

          a = 2513.27² 0.633

          a = 3.998 10⁶ m / s²

the linear and angular variable are related

          a = α r

          α = a / r

          α = 3.998 10⁶ / 0.633

          α = 6.31 10⁶ rad / s²