xissburg

Consider a cylinder with radius \( r \) and length \( \ell \) whose axis contains points \( \mathbf{q}_0 \) and \( \mathbf{q}_1 \). Let \( \mathbf{L}(t) = \mathbf{p}_0 + t (\mathbf{p}_1 - \mathbf{p}_0) \) be a line passing through points \( \mathbf{p}_0 \) and \( \mathbf{p}_1 \), and \(... [Read More]

A capsule can be decomposed into a cylinder and two hemispheres, where each hemisphere sits on a cylinder cap. The moment of inertia of a capsule can be calculated as a composition of the moment of inertia of a cylinder and the moment of inertia of a hemisphere. [Read More]

The moment of inertia of a shape about an axis of rotation is equals to the integral of the density \( \rho \) times the squared distance of each point \( \mathbf{p} \) from the axis over the entire volume of the shape. Let \( \mathbf{r} \) be the vector... [Read More]

Consider a hemisphere of radius \( R \) with its bottom face centered at the origin, laying on the \( xz \)-plane, where the \( y \) axis points up. [Read More]

The moment of inertia of a shape about an axis of rotation is equals to the integral of the density \( \rho \) times the squared distance of each point \( \mathbf{p} \) from the axis over the entire volume of the shape. Let \( \mathbf{r} \) be the vector... [Read More]