3.1. Representation of vectors

Try these first

1. 1.

   What is a vector?

   Hint

   Think about how a force is represented.

2. 2.

   Describe the significance of coordinate systems in vector representation.

   Hint

   Recall the alignment of vectors.

3. 3.

   What is a vector?

   • A quantity with magnitude only
   • A quantity with direction only
   • A quantity with both magnitude and direction

   Hint

   Consider what a force acts as.

4. 4.

   The stress tensor is dependent on the choice of planes used in its derivation.

   • True
   • False

   Hint

   Recall the definition of the stress tensor.

5. 5.

   Given a vector represented in a standard coordinate system, derive its representation in a rotated coordinate system and explain the implications of this change in terms of stresses.

   Hint

   Consider how trigonometric functions relate the two coordinate systems.

6. 6.

   Design a simple experiment to demonstrate how the representation of a stress tensor might differ based on the outside loading conditions of a material.

   Hint

   Make sure to visualize the stress tensor in tabular form based on readings obtained.