Gyroscope. The gyroscope apparatus could easily malfunction or produce incorrect results. It should be treated with extra care.

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General Physics Lab Department of PHYSICS YONSEI University Lab Manual (Lite) Gyroscope Ver.

For more information and full instructions of the experiment, see the FULL version of manual.

It should be treated with extra care. 1.

Subjecting the apparatus to strong impact could cause the sensors to fail, or the axles to be bent. 3. Never touch the sensor modules.

1 General Physics Lab Department of PHYSICS YONSEI University Lab Manual (Lite) Gyroscope Ver NOTICE This LITE version of manual includes only experimental procedures for easier reading on your smartphone. For more information and full instructions of the experiment, see the FULL version of manual. Gyroscope Procedure Caution The gyroscope apparatus could easily malfunction or produce incorrect results. It should be treated with extra care. 1. Keep tight hold of the gyroscope axle while you pull the thread to rotate the flywheel, or while you stop the flywheel. 2. Subjecting the apparatus to strong impact could cause the sensors to fail, or the axles to be bent. 3. Never touch the sensor modules. Note You will use two kinds of thread/string in this experiment. Use Thread For suspending a weight from the flywheel pulley (Experiment 1) String For spinning up the flywheel of the gyroscope (Experiment 2 ~ 5) Where Lecture Table Each Lab Table Wound on a spool Thicker one with loops Shape Color: Black or White Note Do NOT cut the string. Do NOT untie endknots.

Experiment 1. Moment of Inertia of Flywheel (1) Set up equipment. 1 Clamp the gyroscope axle.

Assemble the photogate assembly (the raised slot on the photogate housing provides a seat for attaching a pulley using a pulley

Tie a length of thread to the hole of the pulley of the flywheel. Tie a mass of 50g at the other end of the thread.

Adjust the position of the photogate pulley so the thread runs parallel to the table and the weight can fall out of the table.

2 Experiment 1. Moment of Inertia of Flywheel (1) Set up equipment. 1 Clamp the gyroscope axle. Using a support rod and a multi-clamp, clamp the gyroscope axle in the horizontal position. 2 Install the photogate assembly. Assemble the photogate assembly (the raised slot on the photogate housing provides a seat for attaching a pulley using a pulley mounting post). And then mount it on the support rod using a multi-clamp. 3 Arrange a weight to accelerate the flywheel. Tie a length of thread to the hole of the pulley of the flywheel. Tie a mass of 50g at the other end of the thread. And then pass the thread over the photogate pulley. 4 Adjust the position of the photogate pulley. Adjust the position of the photogate pulley so the thread runs parallel to the table and the weight can fall out of the table. 5 Adjust the length of the thread, if required. The weight must stop falling before it reaches the ground. 6 Connect the Photogate to the interface. (2) Configure the Capstone software. 1 Add [Photogate with Pulley]. (Make sure you do not select [Photogate].)

is 0.015m, and the spoke angle is 36. 3 Create a graph display.

pulley, until the weight is located near the photogate pulley.

3 2 Create a timer. Make sure that [Linear Speed] is checked, the spoke arc length is 0.015m, and the spoke angle is Create a graph display. xx-axis: [Time(s)], yy-axis: [Linear Speed(m/s)] (3) Wind the thread around the pulley. By rotating the flywheel, wind the thread around of the pulley, until the weight is located near the photogate pulley. (4) Click [Record]. (5) Release the flywheel. The torque of a tension force rotates the flywheel. Click [Stop] before the weight reaches the ground.

(6) Find the acceleration aa of the system. (7) Calculate II of the flywheel. II = mmrr 2 gg 1 (12) aa mm 0.

1 st 2 nd 3 rd average mm (kg) rr (m) aa II (9) Compare the result with the theoretical value.

Measure the mass, the inner radius, and the outer radius of the flywheel, and calculate the theoretical value II flywheel of the flywheel.

it. If required, use the pre-calculated value II pulley = 5.51 10 5 kg m 2. Experiment 2. Motion of Gyroscope, Part 1 (1) Set up equipment.

4 (6) Find the acceleration aa of the system. (7) Calculate II of the flywheel. II = mmrr 2 gg 1 (12) aa mm kg : Mass of the weight rr m : Radius of the pulley (8) Repeat the measurement. Repeat the steps (3) to (7) more than three times. 1 st 2 nd 3 rd average mm (kg) rr (m) aa II (9) Compare the result with the theoretical value. The flywheel part is prepared on lecture table. Measure the mass, the inner radius, and the outer radius of the flywheel, and calculate the theoretical value II flywheel of the flywheel. RR 1 = (m) RR 2 = (m) MM = (kg) Because the moment of inertia of the pulley is relatively smaller than that of the flywheel, you can ignore it. If required, use the pre-calculated value II pulley = kg m 2. Experiment 2. Motion of Gyroscope, Part 1 (1) Set up equipment. 1 Remove the photogate assembly. 2 Remove the support rod and the multi-clamp clamping the gyroscope axle. 3 Remove the thread connected to the weight. (2) Balance the gyroscope axle in the horizontal position. Adjust the position of the counterweights until the gyroscope is balanced without an add-on mass.

(4) Observe the motion of the gyroscope with rotating. Spin the flywheel. And then tap the end of the gyroscope axle in the horizontal direction.

5 (3) Observe the motion of the gyroscope without rotating. Do not spin the flywheel. Tap the end of the gyroscope axle in the horizontal direction, and observe the motion of the gyroscope. (4) Observe the motion of the gyroscope with rotating. Spin the flywheel. And then tap the end of the gyroscope axle in the horizontal direction. Observe the motion of the gyroscope. (5) Compare the results. Q Describe the differences of two cases and explain why. A Caution When you stop the spinning flywheel, follow the instructions below. Experiment 3. Motion of Gyroscope, Part 2 (1) Spin the flywheel.

(2) Apply a steady force on the gyroscope axle. With the flywheel rotating, pull the gyroscope axle downward using a string (or push it downward using your finger).

A Q If you change the direction of the force, which direction is the axle going in? Explain why. A Experiment 4.

(1) Set up the equipment. Connect the gyroscope apparatus to the computer using Serial USB cable. Provide power to the apparatus using 12V DC adapter.

6 (2) Apply a steady force on the gyroscope axle. With the flywheel rotating, pull the gyroscope axle downward using a string (or push it downward using your finger). Observe the motion of the gyroscope. Q Can you simply swing the gyroscope axle as you pull it? If not, which direction is the axle going in? Explain why. A Q If you change the direction of the force, which direction is the axle going in? Explain why. A Experiment 4. Precession Angular Speed Caution Before you run SensorLAB, you should shut down PAS- CO Capstone. If not, they suddenly crashes and you may lose your experimental data. (1) Set up the equipment. Connect the gyroscope apparatus to the computer using Serial USB cable. Provide power to the apparatus using 12V DC adapter. (Different type of DC adapter can be provided.) (2) Run SensorLAB software. 1 Connect or disconnect communication. 2 Begin or stop recording. 3 Displays the sensor readings. 4 Plots graphs. 5 Select graph type. 6 Span graphs. 7 Converts the value of rotating angle to absolute value. 8 Change the sign of sensor values. 9 Adjust the ranges. 10 Shows data table.

(2-1) Click [Connect] to receive the sensors values. [Received Data] displays the real-time values of the sensors.

the RPM sensor) (2-2) Set [Absolute Value].

[Received Data] and rotate the rotating axle of the gyroscope clockwise or counterclockwise.

(2-3) Set [Flip Horizontal] and [Flip Vertical]. [Rotation] value initially increases when the rotating axle of the gyroscope rotates counterclockwise.

7 (2-1) Click [Connect] to receive the sensors values. [Received Data] displays the real-time values of the sensors. Rotation : Rotating angle of the rotating axle ( ) (by the rotary motion sensor) Tilt : Tile of the gyroscope axle ( ) (by the tilt sensor) DiskRPM : RPM of the flywheel (revolutions per minute) (by the RPM sensor) (2-2) Set [Absolute Value]. By [Absolute Value] icon, [Rotation] value will [Continually increase regardless of the rotating direction] [increase or decrease according to the rotating direction] Watch the [Rotation] values of [Received Data] and rotate the rotating axle of the gyroscope clockwise or counterclockwise. If [Rotation] value continually increases regardless of the rotating direction, depress [Absolute Value] icon. Then it will increase or decrease according to the rotating direction. (2-3) Set [Flip Horizontal] and [Flip Vertical]. [Rotation] value initially increases when the rotating axle of the gyroscope rotates counterclockwise. If you depress [Flip Horizontal] button, [Rotation] increases when the axle rotates clockwise. [Tilt] value is initially positive when the arm with the flywheel of the gyroscope axle is higher. If you want to change the sign of [Tilt], depress [Flip Vertical]. (2-4) Select a graph type. You can change graph types to display on the graph area. Select any type of graph in [Graph Option]. The data collection will automatically end when the graph point reaches the right end of the graph display. It is not recommended to select the [Rotation-Tilt] graph because the data collection finishes in a relatively short time. (This graph type is for the 5 th experiment, nutation.) Select a flow mode graph type by depressing [Flow mode] icon. (2-5) Set the range of each axis. Set the range of xx-axis (time) at maximum (60 seconds). The data collection will automatically end after 60 seconds.

(3) Level the gyroscope. Follow the steps below. Do not move the apparatus after finishing leveling it. (4) Balance the gyroscope axle. The counterweight arm has three weights.

Note In this experiment, you will use the gyroscope equipped with several sensors and components on the gyroscope axle. They all act downward force in the yy-direction.

If the axle is exactly balanced in the horizontal position by adjusting the position of counterweights, we don t have to consider the torque of any component (including the flywheel) on the axle.

8 (3) Level the gyroscope. Follow the steps below. Do not move the apparatus after finishing leveling it. (4) Balance the gyroscope axle. The counterweight arm has three weights. Adjust the positions of these weights so that the gyroscope axle is exactly balanced in the horizontal position. Note In this experiment, you will use the gyroscope equipped with several sensors and components on the gyroscope axle. They all act downward force in the yy-direction. Because we do not know their weights and distances from the pivot, we cannot calculate net torque. If the axle is exactly balanced in the horizontal position by adjusting the position of counterweights, we don t have to consider the torque of any component (including the flywheel) on the axle. Instead, to produce the turning torque, you will attach an add-on weight to the front of the flywheel. Then you can easily calculate the torque by measuring the mass and the position of the add-on weight. (5) Spin the flywheel. Spin up the flywheel to high speed using the string. (6) Hang an add-on weight. To produce a tipping torque, hang the 100g weight on the RR = 0.15 m hanger. (The hangers are 0.15, 0.17, 0.19, and 0.21 m away from the pivot.)

(7) Let the gyroscope precess. If you spin the flywheel in the direction as shown above, the gyroscope will precess counterclockwise. In the general case, i.e. for arbitrary initial conditions, the motion of the gyroscope is a superposition of precession and nutation.

This deviation is absent only for carefully chosen specific initial conditions.

release gently. If you touch the end of the axle, you can feel the speed of the gyroscope.

If you push it faster or slower than the correct speed, it will move upward or downward. When it precesses without nutation, begin data collection.

9 (7) Let the gyroscope precess. If you spin the flywheel in the direction as shown above, the gyroscope will precess counterclockwise. In the general case, i.e. for arbitrary initial conditions, the motion of the gyroscope is a superposition of precession and nutation. Nutation is caused by a possible small deviation of the vector of own angular momentum from the axis of symmetry. This deviation is absent only for carefully chosen specific initial conditions. It means you have to help the gyroscope start precessing with the gyroscope axle horizontal by moving it along in the correct direction at the correct speed, and then release gently. If you touch the end of the axle, you can feel the speed of the gyroscope. Help the gyroscope start precessing with the gyroscope axle horizontal by moving it along in the correct direction at the correct speed, and then release gently. If you push it faster or slower than the correct speed, it will move upward or downward. When it precesses without nutation, begin data collection. (8) Begin data collection. Click [Start] to begin data collection. The display will start plotting graph. The data collection will automatically end after 60 seconds (as you set in the step (2-5)). (9) Extract collected data. Click [Datasheet] icon to extract data table Click [Save] to save the data as text format file (*.txt).

(10) Open the data file. You can use Microsoft Excel to import data from a text into a worksheet.

Then, in the Import Text File ( 텍스트파일가져오기 ) dialog box, doubleclick the text file that you want to import.

(11) Analyze the data. Cells in the column B contain the values of the rotating angle of the rotating axle.

08) seconds for one complete turn. The average RPM (rev/min) of the flywheel during this time interval, is given by Average(D9:D1061). (12) Calculate the precession angular speed.

10 (10) Open the data file. You can use Microsoft Excel to import data from a text into a worksheet. To start the Text Import Wizard, on the Data ( 데이터 ) tab, in the Get External Data ( 외부데이터가져오기 ) group, click From Text ( 텍스트 ). Then, in the Import Text File ( 텍스트파일가져오기 ) dialog box, doubleclick the text file that you want to import. In the step 1 of 3 of the Text Import Wizard, select Delimited ( 구분기호로분리됨 ) for Original data type ( 원본데이터형식 ). In the step 2 of 3, check Comma ( 쉼표 ) and Space ( 공백 ) for Delimiters ( 구분기호 ). (11) Analyze the data. Cells in the column B contain the values of the rotating angle of the rotating axle. The table below shows that the difference between B9 cell and B1061 cell is 360 degrees (1 complete turn). Column A (time column) shows that it has taken (= ) seconds for one complete turn. The average RPM (rev/min) of the flywheel during this time interval, is given by Average(D9:D1061). (12) Calculate the precession angular speed. Verify equation (11). Ω = dddd dddd = ττ LL = MMggRR IIII (11) Experimental value of the precession angular speed is Ω = 2ππ/TT, where the period TT of the gyroscope is experimentally obtained in the step (11). Theoretical value of the precession angular speed is Ω = MMggRR IIII, where MM is the mass of the add-on weight, RR is the distance from the pivot to the add-on weight, II is the moment of inertia of the flywheel which is obtained in the experiment 1, and ωω is the flywheel angular speed which is obtained in the step (11). (1 rpm = 1 rev/min = 1/60 rev/s = 2ππ 60 rad/s) (13) Repeat experiments. Vary conditions and repeat experiment. MM RR II ωω Ω = MMggRR IIII Ω = 2ππ TT 1 st 2 nd 3 rd

Experiment 5. Nutation Change [Graph Option] to [Rotation-Tilt].

With the add-on weight producing a tipping torque, hold the axle horizontally, and then 1 Gently tap it in the

gyroscope undergoes nutation, as in patterns below.

Delete your data files from the lab computer. Turn off the Computer and the Interface.

11 Experiment 5. Nutation Change [Graph Option] to [Rotation-Tilt]. Spin up the wheel to high speed using the string. With the add-on weight producing a tipping torque, hold the axle horizontally, and then 1 Gently tap it in the counter-precession direction 2 Suddenly release it from rest 3 Gently tap it in the precession direction The gyroscope undergoes nutation, as in patterns below. End of LAB Checklist Please put your equipment in order as shown below. Delete your data files from the lab computer. Turn off the Computer and the Interface. Keep the Gyroscope Apparatus away from strong impact. Never touch the sensor units of it. Unplug the Gyroscope DC Adapter. Do not unplug the Serial-USB Cable from the computer. Be careful not to knot or tangle the String. Keep the Flywheel Parts, Spools of Thread, Scissors in the basket on the lecture table at the font of the laboratory.

Instruction Manual No A. Goniometer PS-2138, PS-2137

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