 Solution

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2017-resit/11/b/solution

For a uniform disk, the surface mass density is

σ = m / (π a^{2})

. Integrate concentric annuli of mass

d m = 2 πσ r d r

about the central perpendicular axis:

I_{O} = \int_{0}^{a} r^{2} (2 πσ r d r) = \frac{πσ a ^{4}}{2} = \frac{1}{2} m a^{2} .

The result is specific to a uniform thin disk and that axis; it is not the diameter-axis moment of inertia, which is

m a^{2} /4

 New to topics? Read the docs here!