Answer:
The total moment of inertia is [tex]I_ t =0.01704 \ kg \cdot m^2[/tex]
Explanation:
From the question we are told that
The diameter of the core is [tex]d = 0.196 \ m[/tex]
The mass of the core is [tex]m_c = 1.6 \ kg[/tex]
The mass of the shell is [tex]m_s = 1.6 \ kg[/tex]
The diameter of the shell is [tex]d_s = 0.206 \ m[/tex]
Generally the radius of the core is
[tex]r_c = \frac{d}{2}[/tex]
=> [tex]r_c = \frac{ 0.196 }{2}[/tex]
=> [tex]r_c = 0.098 \ m[/tex]
Generally the radius of the shell is
[tex]r_s = \frac{d_s}{2}[/tex]
=> [tex]r_s = \frac{ 0.206 }{2}[/tex]
=> [tex]r_s = 0.103 \ m[/tex]
Generally the total moment of inertia is mathematically represented as
[tex]I_ t = I_c + I_s[/tex]
Here [tex]I_c[/tex] is the moment of inertia of the core which is mathematically represented as
[tex]I_c = \frac{2}{5} * m_c * r_c^2[/tex]
=> [tex]I_c = \frac{2}{5} * 1.60 *(0.098)^2[/tex]
=> [tex]I_c = 0.01024 \ kg \cdot m^2[/tex]
and [tex]I_s[/tex] is the moment of inertia of the shell which is mathematically represented as
[tex]I_s = \frac{2}{5} *m_s * r_s^2[/tex]
=> [tex]I_s = \frac{2}{5} * 1.60 *(0.103)^2[/tex]
=> [tex]I_s = 0.0068 \ kg \cdot m^2[/tex]
So
[tex]I_ t = 0.01024 + 0.0068[/tex]
=> [tex]I_ t =0.01704 \ kg \cdot m^2[/tex]
