Uniform Circular Motion Apparatus

An apparatus was constructed to demonstrate and accurately prove that centripetal acceleration is proportional to radius and square of angular speed in uniform circular motion, in an elegant and creative way. Electronics on the rotation stage sense both angular speed and radial acceleration simultaneously. The apparatus reports the results using a persistence of vision display, made with light-emitting diodes, rotating with the stage. This eliminates the need for wired or wireless connection between the rotating stage and a stationary data acquisition system for relaying data. The entire system is controlled by an Arduino microcontroller. The accuracy in angular speed and acceleration are around 2%.

Introduction

Principle of Operation

Pictures

Apparatus construction pictures

Arduino Microcontroller and Software

Why Did We Design This Apparatus?To address the following issues:

Data and errorThe range of angular speed is 1.2 rev/s to 4.2 rev/s.The range of acceleration is up to 18g.The range of radius is up to 22cm.The relative error of angular speed is within 2%.The relative error of acceleration is around 2% at 20cm radius.The absolute error of radius is around 1mm.

Conclusions and future directions

Our demonstration apparatus is accurate enough for quantitative analysis of uniform circular motion.Our apparatus will be effective in qualitatively demonstrating the properties of uniform circular motion.Our apparatus is simple to construct and the program is relatively easy to understand and can be modified to suit other needs.We will pursue more projects and apparatus with accelerometers.We will explore the use of POV displays in public reach.We will consider making more DIY teaching apparatus with Arduino.

• A DC power supply powers a 15V motor to rotate a Pasco stage.

• Hall-Effect magnetic switches are placed on the rotation stage to sense its rotation speed and synchronize the persistence of vision display from a stationary magnet on a poll.

• An accelerometer on the stage senses the radial acceleration.

• Two 8-LED persistence of vision displays output measured results.

• Arduino (homemade) measures and displays the results.• A Pasco photogate can be used to confirm measurement

accuracy.

Saint Cloud State University, St. Cloud, MN 56301

Dr. Zengqiang Liu , Jing Chen, Shunjie Yong, Steve Zinsli

if ((btn_1.sense()==buttons_down)||(btn_2.sense()==buttons_down)){this_trigger=millis();period=this_trigger-last_trigger;last_trigger=this_trigger;if (period>1000) period=100; // This prevents the display from stuck at a low speed.w=1000/(float)(period)/2;abs_level=analogRead(ay_pin);y_level=abs_level-ay_base;a_g=((float)y_level)/gy_factor;if (millis()<30000) sprintf(msg,“ AAPT Omaha 2011");else sprintf(msg," %1d.%02d RPS %2d.%02dg", int(w), int((w-int(w))*100), int(a_g), int((a_g-int(a_g))*100));displayMsg(msg,int(2000/w),1);}

Sense magnetic sensors

Sensor triggered?

NO

Calculate angular speed

(rev/s)YES

Sense and calculate

acceleration

Format and display results

1. Magnet 2. Power supply 3. Accelerometer 4. POV display

5. 9V battery 6. microcontroller 7. Motor 8. Photogate9. Pasco Photogate Smart timer 10. Rotating beam with dual

display

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-4

-2

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RE A

ccel

erati

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%)

Pasco Photogate speed (rev/s)

RE Acceleration vs. Angular Speed

RE acceleration

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RE A

ngul

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peed

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Pasco Photogate speed (rev/s)

RE Angular Speed vs. Angular Speed

RE angular speed

void displayMsg(char msg[], unsigned int delayus, unsigned char spacing){char i=0;while (msg[i]){

displayChar(msg[i],delayus);updateLed(0);delayMicroseconds(delayus);i++;}}

void displayChar(unsigned char ch, unsigned int delayus){for (char i=0;i<5;i++){

updateLed(font[ch-32][i]);delayMicroseconds(delayus);}}

void updateLed(unsigned char first8) {digitalWrite(myLatchPin, LOW); shiftOut(myDataPin, myClockPin, LSBFIRST, first8);digitalWrite(myLatchPin, HIGH);}

displayMsg(char [], unsigned int)

displayChar(unsigned char, unsigned int)

updateLED(unsigned char)

y = 0.203x2 + 0.0264x - 0.2324R² = 0.9998

0.0

50.0

100.0

150.0

0.0 10.0 20.0 30.0

POV

acc

eler

ation

(m/s

^2)

POV angular speed (rad/s)

Acceleration vs. angular speed

Acceleration vs. angular speed

Poly. (Acceleration vs. angular speed)

Uses human persistence of vision (POV) to display information

Uses a column of LED, similar to a dot-matrix printerSynchronized by Hall Effect magnetic switchOnly gets persistence above 2Hz refresh rateNo need for wired or wireless data download or

transferKids think it looks very coolDisplays anything made of dotsCheap to constructLimited display areaOnly works on rotating stagesDifficult to photograph

The Apparatus

Persistence of Vision Display

a=w2r?Students have trouble grasping this formulaDifferential calculus doesn’t help explaining the

concept.Our lab apparatus is not effective to help our

students.We need sufficient data points to show this relation.We only want to spend a small amount of money.We want to make it cool, so we can use it in outreach

as well

Google.com

What is an Arduino?Arduino is a cheap open-source, easy to use

microcontroller boardArduino can read sensors such as buttons, thermistors,

photogates, sonic rangers, accelerometers, Hall Effect switches, GPS etc.

Arduino runs programs without the need of a PCArduino talks to a PC via serial port or displays on LCDArduino uses C/C++ for programmingArduino has an active online communityArduino is used by artists and beginner hobbyistsArduino projects

Main programy = 0.2038x - 0.0519

R² = 0.9998

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150

0 200 400 600 800

Acc

eler

ation

(m/s

2 )

(Angular speed)2 (rad2/s2)

Acceleration vs. (angular speed)2

Acceleration

Linear (Acceleration)

Persistence of vision subroutines

Hall probe Magnet

on a poll

Dot-matrix printer output

POV display head

Sample display message

Connections:• Analog pin 0: accelerometer

output• Digital pin 8: Hall Effect switch 1• Digital pin 9: Hall Effect switch 2• Digital pin 10: Shift register

clock• Digital pin 11: Shift register

latch• Digital pin 12: Shift register data

Picture captions:• (A) Complete setup picture• (B) Breadboard prototype connection

diagram• (C) POV head on printed circuit board• (D) Low-cost DIY Arduino board• (E) Test run result: w=2.34rev/s and

a=4.47g• (F) Accelerometer and L-bracket

For details and complete project code email zliu@stcloudstate.edu

Arduino compatible board $13Accelerometer (±18g range) $1874HC595 shift registers (2pcs) and Bright LEDs

(16pcs) $2Hall Effect magnetic sensors (2pcs) and small

magnets (2pcs) $4Wires and perforation boards or PCBs $4-$12Pasco rotation stage with 15V DC motor15VDC adjustable student power supplyBasic computer for data analysis and programming

ArduinoSoldering iron, wire cutter

Parts list

(A)

(B)

(C)

(D)

(E)

(F)