Experiment 3: conservation of angular momentum, Purpose, Theory – PASCO PS-2120A Rotary Motion Sensor User Manual
Page 15
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P S - 2 1 2 0 A
E x p e r i m e n t 3 : C o n s e r v a t i o n o f A n g u l a r M o m e n t u m
15
E x p e r i m e n t G u i d e
Experiment 3: Conservation of Angular Momentum
*Click the equipment item to go to the PASCO web site.
Purpose
A non-rotating 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:
Equipment Required*
Equipment Required*
Interface
Paper clips (for masses <1 g)
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
=