EXPERIMENT 2
CONSERVATION OF ANGULAR MOMENTUM
I. Objectives
✓ To determine Rotational Inertia of Disk and Ring
✓ To determine Conservation of Angular Momentum in the practicum
✓ To determine how much energy has been lost when collision is occurred
II. Scope
Determination of:
1. Inertia of rotating disk and ring as the result of angular acceleration(alpha), mass
of the object, torque, radius and gravity
2. Energy Lost when collision between disk and ring occurred as the result of inertia
in the system and angular velocity
A. Theory
1. Rotational Intertia
The rotational inertia of a disk about its center of mass is given by,
1
𝐼 = 𝑀𝑅2 (eq.2.1)
2
Figure 2.1
Disk about Center of Mass & Diameter
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Where M is the mass of the disk and R is the radius of the disk. The rotational
inertia of a disk about its diameter is given by,
1
𝐼 = 𝑀𝑅2 (eq.2.2)
4
Theoritically, the rotational inertia, I of a ring about its center of mass is given
by :
1
𝐼 = 𝑀(𝑅1 + 𝑅2 )2 (eq.2.3)
2
Where M is the mass of the ring. R1 is the inner radius of the ring, and R2 is
the outer radius of the ring, see figure 2.2
Figure 2.2
Ring outer & inner radius
Figure 2.3
Set-up for Disk and Ring
To find the rotational inertia experimentally, a known torque is applied to the
object and the resulting angular acceleration is measured, Since 𝜏 = 𝐼𝛼
𝜏
𝐼= (eq.2.4)
𝛼
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Where 𝛼 is the angular acceleration which is equal to a/r and 𝜏 is the torque
caused by the weight hanging from the thread which is wrapped around the
base of apparatus,
𝜏 = 𝑟𝑇 (eq.2.5)
Where r is the radius of the cylinder about which the thread is wound and T is
the tension in the thread when the apparatus is rotating. Applying Newton
second law for the hanging mass, m gives
Figure 2.4
Rotational Apparatus and free body diagram
Solving for the tension in the thread gives:
𝑇 = 𝑚(𝑔 − 𝑎) (eq.2.6)
Once the linear acceleration of the mass (m) is determined, the torque and the
angular acceleration can be obtained for the calculation of the rotational
inertia.
2. Conservation of Angular Momentum
When the ring is dropped onto the rotating disk, there is no net torque on the
system since the torque on the ring is equal and opposite to the torque on the
disk. Therefore, there is no change in angular momentum. Angular momentum
conserved
𝐿 = 𝐼𝑖 𝜔𝑖 = 𝐼𝑓 𝜔𝑓 (eq.2.7)
Where 𝐼𝑖 is the initial rotational inertia and 𝜔𝑖 is the initial angular speed.
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Figure 2.5
Dropped Ring - Experiment Setup
Energy Lost when collision occured can be calculate using equation:
1 1
𝐼 𝜔 2 − 𝐼𝑓 𝜔𝑓 2
2 𝑖 𝑖 2
%𝐾𝐸 𝐿𝑜𝑠𝑡 = 1 (eq.2.8)
𝐼𝜔2
2 𝑖 𝑖
B. Reference(s)
Hunt, C. (2012, July 17). Conservation of Angular Momentum Experiment.
Retrieved from PASCO: https://www.pasco.com/prodCatalog/EX/EX-
5517_conservation-of-angular-momentum-experiment
III. Devices
Equipment
No. Code Type Configuration
Name
3-Step Pulley 10, 29 & 48 mm
Sensor Dimension 10x5x3.75 cm
Rotary
Sensor Shaft Dia. 6.35 mm Three-step Pulley 1 pc
1. Motion PS-2120
Resolution ± 0.09°/0.0078 mm Rod Clamper 1 pc
Sensor
Rotational Res. 0.00157 radian
Max. Rotation Rate 30 rev/s
Rotating Disk 1 pc
Disk Diameter 9.5 cm Large Ring (465 g) 1 pc
Rotational Ring Diameter (inside) 5.4 cm 38 cm Pendulum Rod 1 pc
2. CI-6691
Accessory Ring Diameter (outside) 7.6 cm 75 g Masses 2 pcs
Rod Length 38 cm Super Pulley 1 pc
Black Nylon Thread 1 reel
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Equipment
No. Code Type Configuration
Name
3. Calipers SF-8711 Maximum Length 18 cm 1 pc
100 g Mass 3 pcs
50 g Mass 3 pcs
20 g Mass 6 pcs
10 g Mass 3 pcs
Mass and 5 g Mass 3 pcs
4. ME-8979 Mass Hanger 5 g ± 2%
Hanger Set 2 g Mass 3 pcs
1 g Mass 3 pcs
0.5 g Mass 3 pcs
Mass Hanger 4 pcs
Molded Storage Box 1 pc
Super
5. Pulley with ME-9448 Fits tables thick 0 – 2 cm 1 pc
Clamp
Weight 4 kg Large Rod Stand 1 pc
Large Rod
6. ME-8735 Dia. of rods 6.3 – 12.7 mm Leveling Feet 2 pcs
Stand
Dist. between leveling feet25 cm Clamp Screws 2 pcs
Long Steel Length 45 cm
7. ME-8736
Rod Diameter 12.7mm
850 Interface 1 pc
8. Universal UI-5000 USB Cable 1 pc
Interface Power Cable 1 pc
PASCO
9. UI-5400 1 pc
Capstone
IV. Instruction of Laboratory
A. Procedure
1. Mount the Rotary Motion Sensor to a support rod and connect it to the 850
Universal Interface.
2. Design the equipments like Figure 2.4
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3. Open PASCO Capstone file “Practicum 2” on desktop, make sure rotary
motion sensor is connected on hardware setup.
4. Put a mass 20g on the hanging mass which is on certain distance from the
ground, Release the load at initial velocity equals to zero, and record
acceleration data that use by the load to reach the ground. Repeat the
experiment 5 times and then record on Table 2.1.
5. Calculate T, 𝜏, α and I using equation (eq.2.6), (eq.2.5), and (eq.2.4).
6. Calculate average Idisk from 5 times experiment
Table 2.1 Inertia of Disk
Experiment a (m/sec2) T (N) 𝜏 (Nm) α (rad/sec2) I (kg/m2)
1
2
3
4
5
Average I
7. Design the equipments like Figure 2.3 with ring and disk
8. Release the load at initial velocity equals to zero, and record acceleration data
that use by the load to reach the ground. Repeat the experiment 5 times and
then record on Table 2.2
9. Calculate T, 𝜏, α and I using equation (eq.2.6), (eq.2.5), and (eq.2.4).
10. Calculate average Idisk+ring from 5 times experiment
Table 2.2 Inertia of Disk and Ring
Experiment a (m/sec2) T (N) 𝜏 (Nm) α (rad/sec2) I (kg/m2)
1
2
3
4
5
Average I
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11. Design the equipments like Figure 2.5
12. Change sign of rotary motion sensor on hardware setup properties.
13. Spin the disk with angular velocity up to 27-28 rad/s, drop the ring when
angular velocity between 27-28 rad/s.
14. Record the angular velocity before and after ring dropped, Repeat the
experiment 5 times and then record on Table 2.2.
15. Calculate the angular momentum before and after ring dropped using (eq.2.7).
16. Calculate the amount of energy lost during collision happen using equation
(eq.2.8).
Table 2.3 Conservation of Angular Momentum
i f Li Lf
%KE Lost
Experiment (rad/sec) (rad/sec) (kg m2sec-1) (kg m2sec-1)
1
2
3
4
5
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B. Final Reports requirement for minimum grade
1. Explain the conservation of angular momentum and give 2 examples of its
daily application. What makes the conservation of angular momentum differ
from the linear momentum?
2. Draw and analyze the model of the system used in each experiment and its
acting forces.
3. Explain why the angular momentum is conserved but not as well as its energy in
the collision process. Explain what happened to the lost energy.
4. Analyze the experiment data result and relate it to the theory.
5. Analyze whether if having energy without momentum is possible or not, and
vice versa.
6. Explain the function of each equipments used in the experiment.
7. Write your conclusions for each experiment (at least 5).
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V. Attachment
• Radius of 10-hole pulley:
a. r1 = 23.8 mm
b. r2 = 14.4 mm
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