Question

Question #8a776

Answer 1

Definition: The radius-of-gyration is defined such that, for any geometry, the moment-of-inertia (`I`) is simply its mass (`M`) times the square of the radius-of-gyration (`K`).

`I \equiv M.K^2`

`K = \sqrt{I/M}`

[1] Circular Disc: For a circular disc of mass `M` and radius `R`,

[a] Its moment-of-inertia for rotation about an axis passing through its centre and perpendicular to its plane is -

`I_{z} = 1/2 MR^2 = M (R^2/2); \qquad K_z^2 = R^2/2 \rightarrow K_z = R/\sqrt{2}`

[b] Its moment-of-inertia about an axis passing through its centre and parallel to its plane is -
`I_{x} = 1/4 MR^2 = M (R^2/4); \qquad K_x^2 = R^2/4 \rightarrow K_x = R/2`