Conservation of Angular Momentum
Studio Physics I
While driving around the city, your car is constantly shifting gears. You wonder how the
gear shifting process works. Your friend tells you that there are gears in the transmission
of your car that are rotating about the same axis. When the car shifts, one of these gear
assemblies is brought into connection with another one that drives the car’s wheels.
Thinking about a car starting up, you decide to calculate how the angular speed of a
spinning object changes when it is brought into contact with another object at rest. To
keep your calculation simple, you decide to use a disk for the initially spinning object and
a ring for the object initially at rest. Both objects will be able to rotate freely about the
same axis that is centered on both objects. To test your calculation you decide to build a
laboratory model of the situation.
What is the final angular velocity of a disk with an initial angular speed
?
after being connected with a ring initially at rest?
You will use some approximation of the equipment shown below. A computer-interfaced
sensor will be used to measure angular velocity. You should assume that you will be
given the rotational inertia of the ring, disk, etc..
Equipment
PREDICTIONS
We want a mathematical expression for the final angular velocity of the disk (after the ring
is dropped on it) in terms of , the initial angular velocity of the disk (before the ring is
dropped) and the physical characteristics of the system (rotational inertia of the ring,
disk, spool, axel). In order to work toward this expression, use the problem solving
strategy outlined below:
Lab VII - 36
1.
Make two drawings of the situation, one with the disk already spinning and the ring
being dropped, and one after the ring lands on the disk. Label all the angular velocities
and rotational inertias on your picture-assigning variable names to each quantity.
2.
What basic principle of physics will you use to solve this problem? Discuss the
steps one goes through when solving a problem using this principle.
3. You should have decided that you are going to use conservation of angular momentum
to determine the final angular speed of the rotating objects. What are going to take as your
“system”?
4. Are any objects from outside your system interacting with your system? Are there any
external forces acting on the system? If so, label them. Write down any assumptions that
you are making in applying conservation of angular momentum to the system that you
named in #3 above.
5. What is the angular momentum of the system as the ring is released (before that ring
hits the disk)? What is its angular momentum after the ring connects with the disk? Write
the conservation of angular momentum equation for this situation.
6. Double-check your expression above. Make sure that any quantities that are zero are
shown as zero (or not shown at all). If two quantities have the save value at all times,
show this by using one single variable to represent both. For example, if the initial angular
velocity of ring is the same as the initial angular velocity of the disk for all times before
the collision, show that by the variable you assign to them in your algebraic expression.
Make any changes necessary to your expression from #5 above and rewrite it correctly
here.
7. Is any significant angular momentum transferred to or from the system? Would your
answers change if you were to place the ring on the disk rather than dropping it? (That is,
suppose you are holding on to the ring when it hits the disk).
8. What quantity is it that you really wish to determine? (Refer back to the question
statement on page one if necessary!) Use the equations collected in the steps above to
solve for this quantity. (Assume that we will give you the rotational inertial of the disk and
ring- write the expression algebraically.)
9. Decide what measurements you need to make to check your prediction in #8 for
correctness. Describe your measurement plan here. (Assume, we will give you the
rotational inertias when necessary).
Get the file Conservation of Angular Momentum.mbl from the course webpage. It is at
the bottom of the class activities page. This file type only transfers with Internet Explorer.
Do not use Netscape. Make a couple of practice drops of the ring and rough
measurements to be sure your plan will work. You will get better data if you have a
large angular velocity for the disk to start with.
10. Practice dropping the ring onto the disk as gently as possible to ensure the best data.
Observe what happens if the ring is dropped off-center rather than in the center. Is there
any noticeable difference? If so, what? Does your data show the effects of friction in the
bearings of the rotational motion sensor? If so, how? If not, how would you expect it to
show up?
11. How can you modify your measurement plan to minimize the effects of friction in the
rotational motion sensor on your calculations?
12. Suppose you touch the ring to the rotating disk while you are still holding on to the
ring. (Rather than dropping the ring, you sort of place the ring on the disk.) Would you
expect that angular momentum would still be conserved? Why or why not?
MEASUREMENTS
13. Follow your measurement plan. Record your values of initial and final angular
velocity here. What are the uncertainties in your measurements?
ANALYSIS AND CONCLUSIONS
14. The rotational inertia of the disk+spool+shaft is 1.3 x 10-4 kgm2 and the rotational
inertial of the ring is 5.1 x 10-4 kgm2 .
Using your prediction equation from #8, and your measured initial angular velocity,
calculate the final angular velocity of the disk. If your calculation incorporates any
assumptions, make sure you justify these assumptions based on data that you have
analyzed.
15. Did your measurement of the final angular velocity agree with your calculated value?
If you are not within 15%, repeat the measurement and/or speak to your instructor.
What are the limitations on the accuracy of your measurements and analysis?
16. Could you have used conservation of energy to solve this problem? Why or why not?
Use your data to check your answer.