Find moment of inertia of a disc?
if of a solid disc around an axis through the center and perpendicular to the surface (an axle)
radius R, thickness t
mass M = rho (volume) = rho(pi R^2 t)
I = rho *t* integral 2 pi r^3 dr
= t rho (2 pi)R^4/4 = t rho pi R^4/2
but rho t = M/pi R^2
so
I = M R^2/2