2.3. Partial Derivative of Basis Vectors w.r.t. θ

Try these first

1. 1.

   What are the three basis vectors in cylindrical coordinates?

   Hint

   Think about the three dimensions in cylindrical space.

2. 2.

   Explain what happens to e_r as θ increases.

   Hint

   Consider the motion around a central axis.

3. 3.

   What are the basis vectors in cylindrical coordinates?

   • e_r
   • e_θ
   • e_z
   • e_x
   • e_y
   • e_z
   • r
   • θ
   • z

   Hint

   Visualize each coordinate and its direction.

4. 4.

   True or False: The radial vector e_r remains the same as θ changes.

   • True
   • False

   Hint

   Recall how e_r behaves in motion.

5. 5.

   A mass is moving in circular motion with the radius defined by e_r. If θ changes rapidly, analyze the implications on the mass’s linear momentum.

   Hint

   Focus on how the rapid change in θ impacts the forces on the mass.

6. 6.

   Given that e_θ rotates with θ changes, calculate how the rotational velocity affects the resultant force in a cylindrical coordinate system.

   Hint

   Apply the principles of rotational motion and how they interrelate with e_θ.