3. Representation of vectors and second order tensors in a coordinate system

Try these first

1. 1.

   What is a vector?

   Hint

   Think about direction and size.

2. 2.

   How does a vector change when represented in different coordinate systems?

   Hint

   Consider how we express it mathematically.

3. 3.

   What does the representation of a vector depend on?

   • The magnitude only
   • The coordinate system
   • The physical situation

   Hint

   Consider how a position changes depending on your view.

4. 4.

   The stress tensor is a type of what?

   • True
   • False

   Hint

   Think about the definition of tensors versus scalars.

5. 5.

   Given two coordinate systems and a defined vector, derive its representation in the new system and discuss the implications.

   Hint

   Think about angles and coordinate direction changes.

6. 6.

   If you had a cube and measured stress on all faces, how would you calculate the stress tensor from these measurements?

   Hint

   Use the equations for normal σ and shear τ components.