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For a circular lamina of diameter 100mm, calculate the moment of inertia and radius of gyration about any tangent.
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data: d = 100

Calculate: 1) M.I. about tangent:

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$$ \begin{array}{l}{I_{A B}=\frac{\pi}{64} d^{4}+A h^{2}} \\ {I_{A B}=\frac{\pi}{64}(100)^{4}+\pi(50)^{2} \times(50)^{2}} \\ {I_{A B}=24543692.61 \mathrm{mm}^{4}}\end{array} $$

2) Radius of gyration about tangent:

$$ \begin{array}{l}{K_{A B}=\sqrt{\frac{I_{A B}}{A}}} \\ {K_{A B}=\sqrt{\frac{24543692.61}{7853.982}}=\sqrt{3125}=55.90 \mathrm{mm}}\end{array} $$

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