Conservation of Angular Momentum

Conservation of Angular Momentum

Conservation of
Angular Momentum

Introduction

In your study of linear momentum, you learned that, in the absence of an unbalanced external force, the momentum of a system remains constant. In this experiment, you will examine how the angular momentum of a rotating system responds to changes in the moment of inertia, I.

OBJECTIVES

In this experiment, you will

· Collect angle vs. time and angular velocity vs. time data for rotating systems.

· Analyze the q-t and w-t graphs both before and after changes in the moment of inertia.

· Determine the effect of changes in the moment of inertia on the angular momentum of the system.

· Find the moment of inertia of an oddly shaped object.

MATERIALS

Vernier data-collection interface / ring stand
Logger Pro or LabQuest App / balance
Vernier Rotary Motion Sensor / metric ruler
Vernier Rotary Motion Accessory Kit

Pre-lab

1. Mount the Rotary Motion Sensor to the ring stand. Place the 3-tier Pulley on the rotating shaft of the sensor so that the largest pulley is on top (upside down birthday cake). Measure the mass and diameter of the aluminum disk with the smaller hole. Mount this disk to the pulley using the longer machine screw and sleeve (see Figure 1).

Figure 1

2. Connect the Rotary Motion Sensor to the computer interface and open Logger Pro. The default data-collections settings are appropriate for this experiment.

3. (1 point) Spin the aluminum disk so that it is rotating reasonably rapidly, then click “Collect.” Note that the angular velocity gradually decreases during the interval in which you collected data. What is causing the rotation of the disk to slow down?

4. (3 points) From your graph, gather the information required below and calculate the angular acceleration using kinematics.

wo =

wf =

t =

5. (2 points) Now determine acceleration on Logger Pro by obtaining the slope of the w-t graph. Compare this number with your calculated number above.

a = ______

PROCEDURE

1. Obtain the second aluminum disk from the accessory kit; determine its mass and diameter. Position this disk (cork pads down) over the sleeve of the screw. Practice dropping the second disk onto the first so as to minimize any torque you might apply to the system (see Figure 2).

2. Begin the first disk rotating rapidly and begin collecting data. After a few seconds, drop the second disk onto the rotating disk and observe the change in both the q-t and w-t graphs. Record the angular velocity the moment before the “collision” and the moment after.

3. Now pull out the steel disk and record its mass. Measure and record the diameter of both the central hole and the entire disk. Replace the first aluminum disk (the one on the bottom) with the steel disk (and hub) and tighten the screw as before (see Figure 3).

4. Repeat the experiment, dropping the second aluminum disk onto the steel disk. Record the angular velocity the moment before the “collision” and the moment after.

5. Now get a blob of clay. Decide which disk you want initially mounted. Get it spinning (not so fast that the blob is thrown—we want it to stay on the disk), press collect, wait a few seconds and drop the blob onto the disk. Record the angular velocity the moment before the “collision” and the moment after.

Data Tables (17 points)

Aluminum Disk with small hole: Aluminum Disk with large hole and cork pads:

Mass = ______Mass = ______

Diameter = ______Diameter = ______

Radius = ______Radius = ______

Steel Disk with hub: I= 12mro2+ri2

Mass = ______

Inner diameter = ______

Inner radius (ri) = ______

Outer diameter = ______

Outer radius (ro) = ______

wo (rad/s) / wf (rad/s)
2 Aluminum disk collision
Steel/aluminum disk collision
______disk/
(you choose disk on bottom)
blob of clay collision

EVALUATION OF DATA

1. (6 points) Calculate the moments of inertia for each of the 3 disks (show work):

2. (6 points) For the first 2 collisions (disk collisions), determine the total angular momentum before the collision (show work).

Aluminum-Aluminum (before) Steel-Aluminum (before)

3. (6 points) For the first 2 collisions, determine the total angular momentum after the collision (show work).

Aluminum-Aluminum (after) Steel-Aluminum (after)

4. (4 points) How well do your results show conservation of angular momentum? Determine the difference from before to after for each collision.

Aluminum-Aluminum Steel-Aluminum

5. (4 points) Use conservation of angular momentum to determine the moment of inertia of your clay blob. (Show all work.)

6. (5 points) In this experiment, the moment of inertia of the rotating system was changed by adding mass. In what other way could one change the moment of inertia? Describe an example of how this could be done. Explain specifically how this changes I and subsequently produces a change in w .

AP Physics

Conservation of Angular Momentum Lab