Conservation of Angular Momentum Lab
Background:
Just as we think of objects here on earth (cars, baseballs, runners) traveling with a linear velocity, it is more convenient to describe the motion of rotating objects by their angular velocity. Earth is a rotating planet, and therefore we describe its motion using angular velocity.
Consider a bicycle wheel, with at marker attached to the rim, rotating about its axle:
If the marker rotates through angle α in time t, then the angular speed is ω = α/t[DMS1].
The angular velocity ω has magnitude given by (1) and orientation along the axis of rotation (for the wheel in this diagram, perpendicular to this page), using the right hand rule. So ω in this example points out of the page towards you.
Part I: Angular momentum lesson
This part demonstrates the “ice skater” explanation of the conservation of angular momentum. You will need a rotating chair. Sit on the chair with your arms close to your body and have your lab partner slowly spin you around until you are rotating at at a constant angular speed () and angular momentum. Extend your arms and bring them in several times to see what happens.
1) What will happen to the moment of inertia if you extend your arms outward (as far as you can)?
2) What happens to your angular momentum if you extend your arms outward?
3) What happens to the angular velocity if you extend your arms outward?
4) Have a partner spin you around again, but also have another partner time how long it takes to complete one complete revolution with yours arms close to your body. Without stopping extend your arms as far as possible and repeat the timing.
: With arms close to body ______rad/s.
: With arms out ______rad/s.
5) Use the right hand rule to determine the direction of the angular velocity and angular momentum. Does the direction of the angular velocity change?
6) Repeat this procedure, but this time use ~ 3 lb weights in your hand, and begin with your arms extended. When you bring your arms, what will happen to your angular velocity?
Part II: Angular momentum and meteorology
7) Looking down on the North Pole, which way does the earth rotate? South Pole? (Use a globe)
COAM states that if radius X velocity = constant. Put another way, the radius velocity is inversely proportional to the radius. The attached weather maps contain several cyclones with wind speed observations: Where in relation to the center are the strongest winds located? How does COAM apply to this situation?
8) Figure 1 is a wind synopsis for Hurricane Dora.
a)Where are the strongest winds located?
b)Where are the weakest winds located?
c)How is this explained by conservation of angular momentum
d)Where would you find the strongest winds in a tornado? Why?
9) The earth gains angular momentum if winds are easterly, but loses angular momentum if winds are westerly. Using the general circulation diagram, find regions where earth’s angular momentum is increasing and decreasing.
10) If all winds on earth were easterly, what would happen to the rotation rate (ω) of earth?
11) During strong El Nino years, winds become more westerly. Explain using the concept of angular momentum. What effect would this have on ω?
[DMS1]1I presume that his is (1) referred to in the next sentence.