Lesson 34
Rotating Reference Frames, Foucault Pendulum

1) Consider the coordinate system shown in the figure to the right. This question is about understanding these vectors and how you use them to "get a handle on" the centrifugal and Coriolis force terms.

• Given the axes and vectors shown, how would you write out what the angular velocity vector w is in terms of its components along the x and z axes?
• Consider the directions of the x, y (not shown explicitly on the figure), and z axes, which originate at a point of latitude angle l on the surface of the Earth. In what local directions do those vectors point? In other words, suppose you were standing at that coordinate system origin. In what directions (up, down, East, West, etc.) do these axes point?
• Let (x(t),y(t),z(t)) describe the location at time t of a projectile as seen from the coordinate system origin on the surface of the Earth. If you were to launch a projectile at some elevation angle in the due South direction, what approximations do you think would be reasonable to make about the first derivatives of x(t), y(t), and z(t)?
  
  
  
  
  

  2) There is a Foucault (pronounced "foo-koh") pendulum at the Science Museum of Virginia. According to information the museum provides about their Foucault pendulum, it has a cord that is about 29 meters long and its direction of swing changes by about 9.2 degrees per hour. Use this information to estimate the period of the pendulum's swing and the approximate latitude of the museum.

  If there were an identical pendulum set up in Santa's workshop at the North pole, what would be the same and what would be different?
  
  

  
  
  

  3) Suppose you want to make yourself one of those smooth, crushed-ice and fruit slurpee drinks. You put everything into the blender and turn it on. Which choice best describes an expression for the effective force on a small chunk of orange in the mixture?

  1. 
     
  2. 
     
  3. 
     
  4. 
     
  
  
  
  

  ---

  Below is a space for your thoughts, including general comments about today's assignment (what seemed impossible, what reading didn't make sense, what we should spend class time on, what was "cool", etc.):
  
  

  You may change your mind as often as you wish. When you are satisfied with your responses click the SUBMIT button.

  I received no help from anyone on this assignment.
  I received help from someone on this assignment (document in comments section).