Rotary fair

This is a completely optional assignment; I will give a small amount of extra credit (maybe to count against midterm grades) for each question completed. 

You will need to estimate rotation rates (for which a watch would be helpful) and distances (mostly radii) for some of the rides.  I'm not too worried about the actual numbers you come up with, provided they're not unreasonable, so long as you tell me what period, radius, length, etc. you measured and show me how you used that data to calculate the quantity of interest.

  1. Climbing wall
    1. Estimate the speed with which you would hit the ground if you fell off of the climbing wall.  Since this is much less than terminal velocity for falling in air, you're justified in neglecting wind resistance. 
    2. Assuming you didn't land on anything delicate (like your face), how badly injured would you get?  If you're unsure, convert your answer to mph and ask someone who has been in a car crash how it felt.
  2. Ferris wheel
    1. Estimate its angular velocity.
    2. Assuming it's loaded with fat Americans (so you can neglect the comparatively small mass of the seats themselves and of the spokes), estimate the Ferris wheel's moment of inertia.
    3. Estimate the kinetic energy contained in the rotating Ferris wheel.   
  3. Pharaoh ship
    1. Estimate the natural frequency of the ship, treating it as a pendulum.  Treat it as a small angle pendulum even though I think it goes beyond the small angle approximation.
    2. Estimate the actual frequency at which the ride oscillates.
  4. Round up ("wheel of fun")
    1. Estimate the minimum angular velocity required to keep a person from falling off the ride at its top
    2. Estimate the actual angular velocity of the ride.  Hopefully #2 is quite a bit larger than #1.
  5. Dragon wagon
    1. Using conservation of energy arguments, explain to some of the little kids waiting to board the "Dragon wagon" why the roller coaster slows as it goes over the hump on the track.  You will receive no credit on this question if you scare the kids' parents and get yourself thrown in jail.

No particular due date for this: if you turn this in (either electronically or on paper in my mailbox near the physics office or outside my office in Merrill 118) before I submit grades to the registrar I will give you a (small) amount of credit for this.