3. A thin (and uniform) ring with mass=m and radius=R (i.e., it has line density λ=m/(2πR)) is on the plane of ˆn₁, and ˆn₂. As shown in the figure below (suppose ˆn₃ passes through the center of the ring), the mass of a small section is dm=λ*R*dθ. *
【題組】3.2. (4%) Suppose we have a thin (and uniform) disk with mass=m and radius=R (i.e., it has area density σ=m/(πR²)). For this disk, dm = σ*r*dr*dθ. The central moment of inertia I₃₃ is defined as ∫r² dm. (Integrate from θ=0 to θ=2π, and r=0 to r=R). Please calculate I₃₃ for the disk.
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