PHY 2425 – Engineering Physics I

Conservation of Angular Momentum and Rotational Collisions

Leader: _____________________________ Recorder: ___________________________

Skeptic: _____________________________ Encourager: _________________________

Materials

Rotational Dynamics Apparatus (ME-9279A)

Oil-less air compressor

Introduction

In this activity we will carry out several rotational collisions. We will make use of a different rotational motion apparatus than we have used previously. The apparatus we will use for this part of the lab consists of a turntable with two concentric plates which float on air and which can turn independently of each other. The apparatus also has an optical counter that will measure angular velocity.

Safety

1. The compressors can be quite loud. Please run them only when taking data. Earplugs are available if you wish them.

2. The compressors tend to walk across the table. They should be placed on a piece of foam and fixed to the table while in use.

3. The compressors will get quite hot. Avoid touching them.

Procedure

1. Set-up

Make sure that the apparatus is level and that the air line from the oil-less compressor is attached. Verify that the adapter is plugged in. Place the bottom plate on the axis and place a pin in the hole marked “Bottom Disk Valve” next to the turntable. Place the top stainless plate on top of the bottom plate and place a second pin in the hole in the axis of the two plates. When the pin is plugged into the hole marked “Bottom Disk Valve”, the bottom plate will float freely on a cushion of air. When a pin is plugged into the hole in the center of the apparatus, then the top plate will float freely on a cushion of air.

i) Plug in the compressor. Verify that the two plates can rotate independently by spinning them in opposite directions.

ii) Remove the pin in the center of the apparatus. Verify that the two plates now rotate together.

iii) Return the pin to the center of the axis and remove the pin from the hole marked “Bottom Disk Valve”. Verify that the bottom plate doesn’t rotate and the top plate rotates freely.

iv) Return the pin to the hole marked “Bottom Disk Valve” and verify that both disks rotate freely.

2. Gain Familiarity with the Digital Readout

Examine the edge of the plates. You will notice a pattern of alternating black and white stripes. There are two hundred pairs all the way around the disk. The readout counts the number of pairs that go by per second in units of counts/s.

Q1. Explain why the readout is measuring an angular velocity.

Q2. Determine a conversion factor for converting the readout’s display to units of rad/s.

When the switch is in the lower position it records the angular velocity of the lower plate, and when it is in the upper position it records the angular velocity of the upper plate.

Q3. Spin the lower and upper plates at noticeably different speeds. Record the reading for the upper and the lower plate. Note that you will probably need to wait for a second or two once you change the switch for the readout to update.

Q4. Convert the readings you’ve just taken to rad/s.

3. Preliminary Measurements

Q5. Use the electronic balance to determine the mass of each of the plates. Also measure the radius of each of the plates. Record your information in a data table below.

Q6. Assuming the plates are disks, calculate the moment of inertia for each. Add this information to your data table in Q5.

4. Conduct Rotational Collisions

We will now carry out six different rotational collisions. All six of the collisions will be perfectly inelastic collisions, in that the two plates will move together after the collision. To conduct the collisions we will start with both pins in so that each plate moves independently. We will spin them independently as specified in table 1 below, then we will remove the pin from the center of the apparatus to drop the top plate onto the bottom.

Q7. What is the system for this experiment?

Q8. What is the point of floating the disks on air?

Q9. Is it a reasonable assumption that no external torques act on the system? Explain.

Q10. Notice that in table 1, in some trials you will spin the top disk clockwise and in others counterclockwise. How will you take this into account when you record the data?

Table 1 Initial Conditions for the Eight Collisions - CW means to spin the disk clockwise and CCW means to spin the disk counter clockwise. 0 means that the disk starts at rest.

Top Disk	w1 – Top Disk	w2 – Bottom Disk
Aluminum	CW	CCW
Aluminum	CCW	CCW
Aluminum	CCW	0
Aluminum	0	CCW
Steel	CW	CCW
Steel	CCW	CCW
Steel	CCW	0
Steel	0	CCW

Carry out the experiments for the different initial conditions given in table 1 and record your data and results in the table below. Be sure to include appropriate units. (You can place the units in the table headings.)

Trial	I1	w1i	L1i = I1w1i	I2	w2i	L2i = I2w2i	Li,tot = L1i + L2i	If = I1 + I2	wf	Lf,tot = Ifwf
1
2
3
4
5
6
7
8

If we can ignore external torques, then the total angular momentum of the system is conserved.

Q11. We define DL = L_f,tot – L_i,tot. If total angular momentum is conserved, then what is DL?

Q12. The percent change of angular momentum is defined as . If total angular momentum is conserved, then what should be the percent change of angular momentum?

Q13. Complete the following table for each trial.

Trial	DL	Percent Change
1
2
3
4
5
6
7
8

Q14. Does this experiment suggest that angular momentum was conserved? If not explain which of the assumptions that we made for angular momentum to be conserved didn’t hold.

Q15. Note that some trials will give better results than others. Do you see a trend in the trials that give worse results? What about these trials will tend to amplify the error?