Uniform Circular Motion Apparatus
Dr. Zengqiang Liu , Jing Chen, Shunjie Yong, Steve Zinsli
Saint Cloud State University, St. Cloud, MN 56301
Introduction
Apparatus construction pictures
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 lightemitting 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%.
Why Did We Design This Apparatus?
Pictures
To address the following issues:
(A)
(C)
(E)
a=w2r?
 Students have trouble grasping this formula
 Differential 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
Parts list
Principle of Operation
• 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.
(D)
(F)
(B)
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Arduino compatible board $13
Accelerometer (±18g range) $18
74HC595 shift registers (2pcs) and Bright LEDs (16pcs) $2
Hall Effect magnetic sensors (2pcs) and small magnets (2pcs) $4
Wires and perforation boards or PCBs $4-$12
Pasco rotation stage with 15V DC motor
15VDC adjustable student power supply
Basic computer for data analysis and programming Arduino
Soldering iron, wire cutter
The Apparatus
Data and error
3
6
4
9
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
1
8
7
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
The
The
The
The
The
The
Arduino Microcontroller and Software
10
What is an Arduino?
Main program
 Arduino is a cheap open-source, easy to use microcontroller board
 Arduino can read sensors such as buttons, thermistors, photogates,
Persistence of Vision Display
 Uses human persistence of vision (POV) to display information
 Uses a column of LED, similar to a dot-matrix printer
 Synchronized by Hall Effect magnetic switch
 Only gets persistence above 2Hz refresh rate
 No need for wired or wireless data download or transfer
 Kids think it looks very cool
sonic rangers, accelerometers, Hall Effect switches, GPS etc.
 Arduino runs programs without the need of a PC
 Arduino talks to a PC via serial port or displays on LCD
 Arduino uses C/C++ for programming
 Arduino has an active online community
 Arduino is used by artists and beginner hobbyists
Arduino projects
Sense
magnetic
sensors
Sensor
triggered?
YES
Calculate
angular speed
(rev/s)
Sense and
calculate
acceleration
Format and
display results
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);}
displayMsg(char [], unsigned int)
Sample display message
displayChar(unsigned char, unsigned int)
updateLED(unsigned char)
Hall probe
Magnet
on a poll
Dot-matrix
printer output
POV display
head
Google.com
100
0
-1
50
-2
0
1
2
3
4
Linear (Acceleration)
5
0
0
NO
 Limited display area
 Difficult to photograph
1
Pasco Photogate speed (rev/s)
 Cheap to construct
 Only works on rotating stages
y = 0.2038x - 0.0519
R² = 0.9998
Acceleration
Persistence of vision subroutines
 Displays anything made of dots
150
RE angular speed
RE Angular Speed(%)
3. Accelerometer
4. POV display
7. Motor
8. Photogate
10. Rotating beam with dual display
Acceleration vs. (angular speed)2
RE Angular Speed vs. Angular
Speed
2
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);}
For details and complete project
code email zliu@stcloudstate.edu
200
400
(Angular speed)2 (rad2 /s2 )
600
800
Acceleration vs. angular speed
RE Acceleration vs. Angular Speed
150.0
4
RE acceleration
RE Acceleration (%)
1. Magnet
2. Power supply
5. 9V battery 6. microcontroller
9. Pasco Photogate Smart timer
range of angular speed is 1.2 rev/s to 4.2 rev/s.
range of acceleration is up to 18g.
range of radius is up to 22cm.
relative error of angular speed is within 2%.
relative error of acceleration is around 2% at 20cm radius.
absolute error of radius is around 1mm.
Acceleration (m/s2 )
5
y = 0.203x2 + 0.0264x - 0.2324
R² = 0.9998
2
POV acceleration(m/s^2)
2
100.0
0
-2
50.0
Acceleration vs.
angular speed
Poly. (Acceleration
vs. angular speed)
-4
0
1
2
3
Pasco Photogate speed (rev/s)
4
5
0.0
0.0
10.0
20.0
POV angular speed (rad/s)
30.0
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.