1.1. Basis Vectors

Try these first

1. 1.

   What are the three basis vectors in a cylindrical coordinate system?

   Hint

   Think about the three dimensions represented.

2. 2.

   How does e_z behave compared to e_r and e_θ?

   Hint

   Consider which vector does not change as we rotate.

3. 3.

   Which basis vector remains unchanged regardless of θ?

   • e_r
   • e_θ
   • e_z

   Hint

   Consider which direction is fixed in the coordinate system.

4. 4.

   True or False? The basis vectors e_r and e_θ are constant for all points in a cylindrical coordinate system.

   • True
   • False

   Hint

   Recall that they depend on the angle of rotation.

5. 5.

   Consider a cylindrical object being rotated at constant angular velocity. Analyze how the basis vectors affect the tangential and radial forces acting on the surface.

   Hint

   Think about how forces apply differently across the directions of e_r and e_θ.

6. 6.

   Evaluate the stress transformations occurring within a cylindrical element subjected to internal pressure. Explain how basis vectors influence stress distribution.

   Hint

   Map out the stresses concerning each basis vector to grasp the interactions clearly.