PS-3220
Experiment 3: Conservation of Angular Momentum
21
013-15949A
Experiment 3: Conservation of Angular Momentum
*See the PASCO Web site at www.pasco.lcom for more information
Purpose
A non-rotating thin ring is dropped onto a rotating disk, and the final angular speed of the system is compared with
the value predicted using the principle of the conservation of angular momentum.
Theory
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 (
L
) is conserved.
where
I
i
is the initial rotational inertia and
i
is the initial angular speed of the disk and
I
f
is the final rotational inertia
and
f
is the final angular speed of the disk and the ring together.
The rotational inertia of a disk is given as:
and the final rotational inertia of a disk and ring together is:
where
M
1
is the mass of the disk,
M
2
is the mass of the ring,
R
is the radius of the disk, and
r
1
and
r
2
are the inner
and outer radii of the ring.
Based on this, the final rotational speed is given by:
Setup
1.
Mount the Wireless Rotary Motion Sensor to a support rod. Remove the thumbscrew from the 3-Step Pulley.
Place the disk directly on the square-shaped top of the 3-step Pulley as shown in Figure 3.1.
2.
Place one of the disk alignment guides on the disk. Replace the thumbscrew to the 3-Step Pulley so that the
disk alignment guide is firmly held in place.
Equipment Required*
Equipment Required*
Wireless Rotary Motion Sensor (PS-3220
Base and Support Rod (ME-9355)
PASCO Data Collection Software
Mass and Hanger Set (ME-8979)1
Mini-Rotational Accessory (CI-6691)
Triple Beam Balance (SE-8723)
Calipers (SF-8711)
Paper clips (for masses <1g)
L
I
i
i
I
f
f
=
=
I
i
1
2
---
M
1
R
2
=
I
f
1
2
---
M
1
R
2
1
2
---
M
2
r
1
2
r
2
2
+
+
=
f
M
1
R
2
M
1
R
2
M
2
r
1
2
r
2
2
+
+
-------------------------------------------------------
i
=
