1. Cylindrical Coordinate System

Try these first

1. 1.

   Define cylindrical coordinates.

   Hint

   Think about how we measure distances and angles.

2. 2.

   What are the three basis vectors in cylindrical coordinates?

   Hint

   Remember to think about radial, angular, and vertical directions.

3. 3.

   What are the coordinates used in the cylindrical coordinate system?

   • (x
   • y
   • z)
   • (r
   • θ
   • z)
   • (r
   • φ
   • z)

   Hint

   Remember the terms associated with each direction.

4. 4.

   In cylindrical coordinates, which basis vector remains constant?

   • True
   • False

   Hint

   Think about vertical direction consistency.

5. 5.

   Calculate the total force acting on a cylindrical section with given stress components assuming a specific area and height.

   Hint

   Use the relevant traction vector integrations.

6. 6.

   Design a scenario where the cylindrical coordinate system must be used to analyze forces in a rotating machine component.

   Hint

   Think about how the angle θ influences the force calculations on each face.