Question

Find the radius of gyration of disc about an Axis passing through tangent in plane

Answer 1

Answer:

Not too sure about the wording of the question:

Assuming the axis lies in the plane of the disc and is tangent to the disc:

Ic = 1/4 M R^2   moment of inertia of axis through center and in plane

I = 1/4 M R^2 + M R^2     using parallel axis theorem to get inertia about tangent to disk and in plane of disc

I = 5/4 M R^2 = M k^2    where k is the radius of gyration

k = 5^1/2 / 2

(One can use the "perpendicular axis theorem" to get the moment of inertia about the axis that lies in the plane of the disc and passes through the center of the disc)