Name _____________________
Class ______________
Date _________
Activity P23: Conservation of Angular Momentum
(Photogate)
Equipment Needed
Photogate
Balance (SE-8723)
Base and Support Rod (ME-9355)
Qty
1
1
1
Equipment Needed
Calipers (SF-8711)
Rotational Accessory (CI-6691)
Qty
1
2
What Do You Think?
What interesting sporting events can be understood using the concept of conservation of angular
momentum?
Take time to answer the ‘What Do You Think?’ question(s) in the Lab Report section.
Background
When a net torque is applied to an object that is free to rotate, there is a change in the angular
momentum (∆L) of the object.
L

T
When a non-rotating disk is dropped on a rotating disk, there is no net torque on the system since
the torque on the non-rotating is equal and opposite to the torque on the rotating disk. If there is
no change in angular momentum the angular momentum is conserved:
L  Ii i  I f  f
where Ii and If are the initial and final rotational inertia of the system, with andf being is
the initial and final rotational speed of the system. The initial rotational inertia is that of a disk
and the final inertia is that of the disk and a ring.
The ring has a moment of inertia
I
1
M(R12  R22 )
2
where M is the mass of the ring, R1 is its inner radius, and R2 the outer radius.
The inertia of a solid disk of uniform density is given by
1
I  MR 2
2
where M is the mass of the disk and R is its radius.
For You To Do
The goal in this activity is to measure the initial and final angular speed of a system consisting of
a non-rotating ring that is dropped onto a rotating disk and to verify the conservation of the
angular momentum of the system. Use DataStudio to record and display the linear speed before
and after the torque-free collision.
P23
©1999 PASCO scientific
p. 161
Physics Labs with Computers, Vol. 1
P23: Conservation of Angular Momentum
Student Workbook
012-07000A
PART I: Computer Setup
1.
Connect the DataStudio interface to the computer, turn
on the interface, and turn on the computer.
2.
Connect the photogate phone plug into Digital Channels
1 on the interface.
•
The DataStudio file has a Workbook display and a
Graph display. Read the instructions in the workbook.
PART III: Data Recording
•
In this part of the activity you will drop the ring onto the disk that is attached to the Rotary
apparatus. Hold the ring so that it falls in the groove of the disk.
1.
Place the disk firmly on the rotating system. Give it a spin using
your hand.
2.
Start recording data. (Hint: Click ‘Start’ in DataStudio)
3.
After about 25 data points have been recorded, drop the ring
onto the spinning one.
4.
After another 25 or so data points have been recorded, stop data
recording.
•
Run #1 will appear in the Data list.
5.
Repeat the data recording procedure a total of three times.
p. 162
©1999 PASCO scientific
P23
Name _____________________
Class ______________
Date _________
Analyzing the Data
1
Use the Graph display’s built-in analysis tools to determine the linear speed (Vi) just before
the ring was dropped and the linear speed
(Vf) just after it was dropped. Calculate
the initial angular speed () and the
final angular speed (f) using the
equation:
V = r ω where r is the radius of
the disk with spokes shown to you by
your instructor.
Record them in the Lab Report.
•
In DataStudio, use the ‘Smart Tool’ to
find the coordinates of the point on the
plot just before the second disk was
dropped on the first disk. Then find the
coordinates of the point just after the
second disk was dropped and the two disks are rotating together. The ‘Y-coordinate’ is the
linear speed.
2.
Repeat the data analysis process for each run, selecting the next run from the data list.
Complete the data table by calculating the percent difference between the initial and final
angular momentum of system.
P23
©1999 PASCO scientific
p. 163
Physics Labs with Computers, Vol. 1
P23: Conservation of Angular Momentum
Student Workbook
012-07000A
Record your results in the Lab Report section.
Lab Report – Activity P23: Conservation of Angular Momentum
What Do You Think?
What interesting sporting events can be understood using the concept of conservation of angular
momentum?
Data Table
Item
Value
Radius of disk with spokes ( r )
Ring, inside radius (R1)
Ring, outside radius (R2)
Mass of ring (M)
Moment of inertia of ring
Mass of Disk (M)
Radius of Disk ( R)
Moment of inertia of disk
Moment of inertia of disk + ring
i (rad/s)
Trial
f
(rad/s)
Initial angular
momentum
Final angular
momentum
% Difference
Run #1
Run #2
Run #3
p. 164
©1999 PASCO scientific
P23
Name _____________________
Class ______________
Date _________
Calculations
1
Calculate the values for the initial and final moment of inertia of the system.
2
Calculate the values for the initial and final angular velocity of the system.
3
Calculate the values for the initial and final angular momentum of the system
4
P23
Calculate the percent difference between the two values for the angular momentum.
©1999 PASCO scientific
p. 165
Physics Labs with Computers, Vol. 1
P23: Conservation of Angular Momentum
Student Workbook
012-07000A
Questions
1
How do the two values for the angular momentum agree with each other?
2
What are possible reasons for the difference between the two values of them?
3
A man sits on a spinning piano stool with his arms folded. If he extends his arms, what
happens to his angular velocity? Explain.
4
It is said that a cat always lands on its feet. If a cat starts falling feet up, how can it land
on its feet without violating the law of conservation of angular momentum?
5
A merry-go-round of radius 2 m and moment of inertia 500 kg.m2 is rotating without
friction at 0.25 rev/s. A child of mass 25 kg sitting at the center crawls out to the rim. Find
the new angular velocity of the merry-go-round and the initial and final kinetic energy of
system
p. 166
©1999 PASCO scientific
P23