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
