🧪The Outer Product and Tensor Transformations

Tensors are mathematical objects that generalize scalars and vectors, defined not by their components alone, but by how those components transform under a change of basis, and are formally constructed from outer products of vectors in either the tangent or dual spaces, which determines their type and transformation properties.

1. A disc of mass M and radius R rotating around its symmetry axis with angular velocity

2. The moment of inertia by comparing two discs rotating around different axes

3. the invariance of the Kronecker delta tensor under various coordinate transformations

4. Visualize the curvilinear coordinate through Cartesian grid and a polar coordinate system in a Euclidean space