Physics 124 - Minilab 2 - CONSERVATION OF ANGULAR MOMENTUM
Purpose: To demonstrate the conservation of angular momentum.
DISCUSSION: The picture above shows a rotating disc of mass M and radius R. The timer is used to determine the time for one rotation, T, used to get the angular velocity

. The initial angular momentum Li is the moment of inertia Ii times the initial angular velocity
 i. Then a mass m is carefully dropped onto the rotating disk. The disk with the mass rotates slower at final angular velocity
 f because the new moment of inertia If is now the total of the moments of inertia of the disk and the mass m.
Conservation of angular momentum requires
Li = Lf or equivalently Ii
 i = If
 f.
Initially, we have only the disc rotating, with
Ii = Idisk = 1/2 M R2 , and
 i = 2

/Ti; then we have the disc and mass rotating, with
If = Idisk + Imass = 1/2 M R2 + m r2, and
 f = 2

/Tf.
In this workshop you will find the moments of inertia and the angular velocities, and check that the angular momentum has been conserved: Ii
 i = If
 f.
Procedure
You will use the same software program as last week to obtain data. Login as student, and look in "Course Folders" and then "124" for the lab.
1. Record the mass M and the radius R of the disk, and the small mass m, in the table on the last page of this writeup.
2. Give the disc a slow spin such that it is rotating approximately once every two seconds. Practice dropping the mass onto the disc from as low a height as
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possible, about 1 cm, to see if it stays on the rotating disc. When you have mastered this, remove the mass, and give the disc a slow spin.
3. Start the event timer program, and after a few revolutions do the next step.
4. Now, without disturbing anything, quickly and carefully drop the mass onto the disk from a height of about 1 cm. Dropping the mass near the edge gives good results. If the disk is spinning too fast the mass will fall off.
5. Stop the rotating disc (turn off the air) without disturbing the mass, m. Measure r, the distance between the center of the mass and the axis of rotation. Be careful you do not move the disk while measuring its position.
6. In the data window, read off the time of the last complete revolution before placing the mass on the disk, and the time of the first complete revolution after placing the mass on the disk. Enter these numbers in the table on the last page.
).
Names _______________ _______________ _______________ Section_______
Answer the following questions
1. What is the theoretical value of the ratio Lf / Li? Compare this value with the result of your measurements. Could friction between the mass and the disk account for any discrepancy between theory and experiment? How about friction between the disk and the base?
Explain!
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2. Show that the rotational kinetic energy, K=(1/2) I
 2
, can be expressed as K=(1/2)L 2 / I . If the angular momentum L is conserved, what happens to the kinetic energy in the above experiment? Is K conserved, or does it increase or decrease? Could friction between the mass and the disk account for any change? Explain! disk data
Quantity
M
R
I disk
= (
1/2)
MR 2
Value (units) initial rotation with disk only
T i
(1 Rotation)
 i = 2

/Ti initial angular momentum:
Li = I disk
 i final rotation with extra mass
T f
(1 Rotation)
 f = 2

/Tf
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final angular momentum: ratio: r m
I mass
= m r 2
If = I disk
+ I mass
L f =
If
 f
Lf / Li
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