UNIVERSITY OF ST ANDREWS

Design and construction of an accelerometer-based centripetal force apparatus for the teaching laboratory

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Word count = 3807

Christopher Joseph Lally

4/24/2015

BSc Project

Abstract

Circular motion is a simple concept elegantly described by Newton’s laws of motion. The idea of

centripetal force and acceleration are usually introduced to students using a ball on a string. This

paper examines whether it is useful to use accelerometers to demonstrate the concepts of

centripetal force and acceleration to first and second year physics students. It is definitely possible

to use MEMES accelerometers with an ARM mbed to take measurements of centripetal acceleration,

angular velocity, tangential velocity and even the acceleration due to gravity. However a classical

setup such as that shown in figure 1 could potentially be a better teaching tool as it is more visual.

Figure 1 [1]. Original setup left, Accelerometer setup right

Introduction

The aim of this project was determine whether accelerometers could be used to replace the current

setup of the centripetal force experiment for the first year teaching lab. The current setup is a

classical system based on masses and springs, Figure 1 shows this setup.

In the setup using accelerometers, the masses and springs will all be replaced by two Freescale

differential capacitive accelerometers [2]. The accelerometers work by looking at the difference in

voltage between two sets of capacitor plates, which will be proportional to the acceleration on the

seismic mass. Figure 2 illustrates the inner workings of an accelerometer. Each face of the seismic

mass will have a capacitor plate attached and a corresponding plate parallel to it on the opposite

wall. When a force is felt along one of the X, Y or Z axis the proof mass will move due to Newtons

second law illustrated in Equation 1(F is the force on the mass (𝑁 ), m is the mass of the seismic

mass(𝐾𝑔), and a is the acceleration (𝑚𝑠−2).

Figure 2 [3].

𝐹 = 𝑚𝑎 𝐸𝑞 1.

From the data sheet for the accelerometer it is given that the accelerometer will give an output of

800𝑚V

𝑔 [2], where 𝑚V represents millivolts and g represents 9.81 𝑚𝑠−2 . It is necessary to interface

the accelerometer with a computer to view the output voltage, this was achieved using an ARM

mbed. The mbed is a microcontroller which can be programmed using an application programing

interface (API) based on C/C++ on the mbed developers website [4], in order to achieve various

different functions which can be displayed on a computer or an LCD (liquid crystal display) Figure 3

shows the ARM mbed and its pin configuration[5].

Figure 3. mbed pin map.

When using the mbed with the accelerometers the analogue inputs (pins 15 to 20) are used to read

the output voltage from the X,Y and Z axis of the accelerometer separately . The voltage will appear

as a decimal between 0 and 1, corresponding to 0 V and 3.3 V respectively, therefore it is necessary

to multiply the output by 3.3 in order to retrieve the voltage in Volts. Once the output voltage has

been determined it can be used to calculate the acceleration on each axis and therefore the angular

velocity, linear velocity and the centripetal force on the seismic mass using equations 2-5. This can

be programmed into the mbed and therefore all the calculations will be done by the mbed.( 𝜔

represents the angular velocity in 𝑟𝑎𝑑𝑠−1 , 𝑎𝑐 represents the centripetal acceleration in 𝑚𝑠−2, 𝑣𝑡 is

the tangential velocity 𝑚𝑠−1 and r is the distance between the axis of rotation and the

accelerometer in 𝑚.)

𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑎 =9.81𝑉

0.8 𝐸𝑞 2.

𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝜔 = √𝑎𝑐

𝑟 𝐸𝑞 3.

𝑇𝑎𝑛𝑔𝑖𝑒𝑡𝑎𝑙 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝑣𝑡 = √𝑎𝑐𝑟 𝐸𝑞 4.

𝐶𝑒𝑛𝑡𝑟𝑖𝑝𝑒𝑡𝑎𝑙 𝐹𝑜𝑟𝑐𝑒 = 𝐹𝑐 = m𝑎𝑐 𝐸𝑞 5.

It is also useful to be able to calculate the angular velocity without needing to know the radius r this

can be achieved using equation 6 . 𝑎𝑥2 and 𝑎𝑥1 represent the acceleration at positions X1 and X2

respectively and D id the distance between the accelerometers ,this is illustrated in figure 4 [6].

𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝜔 = √𝑎𝑥2−𝑎𝑥1

𝐷 𝐸𝑞 6 [6].

Figure 4 [6].

The output from the accelerometer does not read zero volts at zero acceleration so a zeroing

process is necessary in order to achieve accurate results, the vale given by the data sheet is between

1.485V and 1.815V with a typical value of 1.65V [2]. So in order to correctly zero each accelerometer

it is first necessary to find the zero-g voltage along each axis and subtract it from the accelerometer

output.

Once the accelerometer has been zeroed it is also necessary to account for random noise, this is due

to fluctuations in the voltage caused by the analogue to digital convertor (ADC) that is built into the

mbed, this can be reduced significantly by averaging the output from the accelerometer using the

mbed. A more effective way to reduce the noise is to use an external ADC with a better noise

performance. An ADS1015 ADC was used to further reduce the noise [7].

In addition to measuring the acceleration using accelerometers a light gate connected to an

oscilloscope was also used to calculate the period of rotation and from this the acceleration and the

angular velocity using equation 3 in addition with equation 7 where f is the frequency of rotation

( 𝑠−1 ) and T is the period of rotation (𝑠) .

𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝜔 = 2πf =2π

T 𝐸𝑞 7.

The light gate was also used with the mbed to allow simultaneous measurements from the

accelerometer and the light gate to allow direct comparison of the results. The output from the light

gate fluctuates from 0V to 5V so it cannot be directly connected to the mbed as it has a maximum

input of 3.3V. To solve this problem an npn transistor was used to reduce the light gate voltage to a

safe level [8]. The circuit used is shown below in figure 5.

Figure 5. Circuit used to reduce the output from the light gate to a safe level for the mbed.

When measuring the acceleration with the accelerometer and the light gate, it was measured as a

function of the drive voltage supplied to the motor driving the rotating platform as the drive voltage

is related to the angular velocity of the platform and therefore the measured acceleration. The drive

voltage was connected to the mbed via a potential divider so the input voltage did not exceed the

mbed max of 3.3V.

Experimental Design & Techniques

Various steps had to be taken in order to mount the accelerometers to the platform .Figure 6 shows

the brackets made to mount the accelerometers to the platform. With this bracket the Z axis of the

accelerometer is aligned parallel to the direction of the centripetal acceleration. The X axis will be

aligned with the acceleration due to gravity and the Y axis will be aligned with the tangential

velocity.

Figure 6. Accelerometer mounted using l shaped bracket. Figure 7. Through bore slip ring.

Figure 7 shows the through bore slip ring, which is necessary to keep electrical contact while

rotating, the slip ring used has six connections. One was used to supply 3.3V to accelerometers one

and two, one was used to ground accelerometers one and two, three were used for the X,Y and Z

connections on accelerometer one and the final connection was used for the Z pin on accelerometer

two. A clamp was also attached to the slip ring as shown in Figure 7 to stop the wires becoming

tangled at high angular velocities. The power was supplied to the motor for the rotating platform by

a power pack via a potentiometer shown in figures 8 and 9.

Figure8. Power Pack. Figure 9. Potentiometer

The potentiometer allows the voltage to be slowly increased or decreased to alter the speed of the

rotating platform.

The Light Gate (shown in figure 10) has a separate power supply (figure 11) and it is also connected

to the oscilloscope, so it can be used to determine the period of rotation.

Figure 10. Light Gate. Figure 11. Light gate power supply.

The light gate, accelerometer and the LCD were all connected up to the mbed, table 1 shows the

wiring map for the mbed. Figures 12 and 13 show the mbed connected to the LCD and the external

ADS1015 ADC respectively.

Figure 12. LCD and ADC connected to mbed. Figure 13. Close up of external ADS1015 ADC.

mbed pin Connected

mbed pin2 connected2

ADS1015 ADC connected4

0V 1 lcd(p1,3,5,16), Acc1(p2), Acc2(p2), ADC(p2) 21 lcd(p11) 1 5V

2 0V

2

22 lcd(p12) 3 SCL

3

23 lcd(p13) 4 SDA

4

24 lcd(p14) 5 5 Collector of transistor from light gate 25

6

6

26

7 Acc1(p5)

7

27 ADC(p3) 8 Acc1(p4)

8

28 ADC(p4) 9 Acc1(p3)

9

29

10 Acc2(p3)

10

30 11

31

12

32 13

33

14

34 15

35

16

36 17

37

18

38 19 lcd(p4) 5V 39 lcd (p2), lcd(p15)

20 lcd(p6) 40 Acc1(p1), Acc2(p1), ADC(p1)

Table 1. Wiring map.

Zeroing the Accelerometers

To zero the accelerometer you must first align the axis you wish to zero perpendicular to gravity, this

was done using a desk mounted clamp. Then you must measure the output voltage while the

accelerometer is static using the mbed. The second step was first done using the ADC within the

mbed and the code used for this process is illustrated in figure 14 (source code can be found in

appendix 1). The levels of noise were not satisfactory so the external ADC was then used. The

process for taking measurements using the external ADC if the same as that shown in figure 14, see

appendix 2 for source code.

Figure 14. Illustrates the function of the code for taking measurements from the accelerometer.

The code used was written on the ARM mbed developer site using the compiler, to load it onto the

mbed you simply select the compile tab and then save the file to the mbed. Then reset the mbed to

start running the file. This programme uses Tera Term Pro to display the accelerometer output on

the computer.

The programmes given in figure 14 will give you values for the voltage at zero acceleration for each

axis when it is perpendicular to gravity. Once you have obtained these values you can take the

average and subtract it from the output of each axis of the accelerometer. The zeroed

Include mbed,X,Y,Z1,Z2 from

accelerometer and the pc

Start

Is I <2400

Yes

No

Stop

Print X,Y,Z1and Z2

acceleration values to

pc

Set I =0

accelerometers can now be used to measure the acceleration due to gravity, centripetal acceleration

and from this the angular velocity.

Taking Measurements

Once the accelerometers had been zeroed the procedure shown in figure 14 was altered to give the

acceleration in 𝑚𝑠−2 and the angular velocity in 𝑠−1 . Appendix 3 shows the code used to take

measurements using the ADC on the mbed; it is similar to the process in figure 14, but I have

introduced averaging to reduce the noise and I have subtracted the zero voltage to give the true

acceleration. The code in appendix 4 was used to measure the acceleration at the same radius on

opposite sides of the rotating platform, to check both accelerometers gave the same centripetal

acceleration when at the same radius. In addition to this the X axis of both accelerometers was

aligned with gravity so the output can be used as a test to check the accelerometer and the code is

working correctly by making sure it reads 9.81 𝑚𝑠−2 . The angular velocity can also be measured

using the light gate and the mbed using the circuit outlined in figure 5 and the code in appendix 5.

Once the measurements have been taken and the results are satisfactory, use the code in appendix

6. This set of commands will allow the student to separately display the acceleration on each axis of

accelerometer one, as well as the angular velocity measured by the light gate when a switch is

turned on. Figure 15 shows the apparatus used to display the data from the experiment on an LCD

screen.

Figure 15. Apparatus used to display various data output from the accelerometer based centripetal force experiment.

Results and discussion

Zeroing with the mbed ADC and the ADS1015 ADC

Graph 1. Used to zero the X-axis of accelerometer 1.

Graph 2. Used to zero the Y-axis of accelerometer 1.

y = 2E-08x + 1.6283

1.59

1.6

1.61

1.62

1.63

1.64

1.65

1.66

1.67

0 500 1000 1500 2000 2500

Voltage (V)

N

Zeroing X axis using mbed ADC

y = -1E-07x + 1.7324

1.69

1.7

1.71

1.72

1.73

1.74

1.75

1.76

1.77

1.78

0 500 1000 1500 2000 2500

Voltage (V)

N

Zeroing Y axis using Mbed ADC

Graph 3. Used to zero the Z-axis of accelerometer 1.

Table 2. Voltage from each axis of accelerometer 1 at zero-g.

Graph 4. Used to zero the X-Axis of accelerometer 1 when using the ADS1015 ADC.

y = 2E-07x + 1.4453

1.42

1.43

1.44

1.45

1.46

1.47

1.48

0 500 1000 1500 2000 2500

Voltage (V)

N

Zeroing Z-Axis using mbed ADC

y = 1E-05x + 1608.9

1590

1595

1600

1605

1610

1615

1620

1625

0 2000 4000 6000 8000 10000

Voltage (mV)

N

Zeroing X-Axis using external ADC

ADC Axis Zero-g Voltage (V) Standard Deviation

mbed X 1.628350625 0.010734988

Y 1.732273125 0.009912746

Z 1.445599375 0.118499763

Graph 5. Used to zero the Y-Axis of accelerometer 1 when using the ADS1015 ADC.

Graph 6. Used to zero the Z-Axis of accelerometer 1 when using the ADS1015 ADC.

y = -7E-05x + 1732.5

1710

1715

1720

1725

1730

1735

1740

1745

1750

0 2000 4000 6000 8000 10000

Voltage (mV)

N

Zeroing external ADC Y1 -axis

y = 0.0003x + 1449.6

1435

1440

1445

1450

1455

1460

1465

0 2000 4000 6000 8000 10000

Voltage (mV)

N

Zeroing external ADC Z1 -axis

Graph 7. Used to zero the Z-Axis of accelerometer 2 when using the ADS1015 ADC.

ADC Axis Zero-g Voltage (mV) Standard Deviation (mV)

ADS1015 X1 1608.986799 5.515565963

Y1 1732.006921 5.1809183

Z1 1450.782129 11.52012144

Z2 1355.342269 4.803923743

Table 3. Voltage from each axis of accelerometer 1 and the z axis of accelerometer 2 at zero-g.

From the data displayed in graphs 1-3 it was possible to zero the X,Y and Z axis of accelerometer 1

when using the ADC within the mbed. The values of Zero-g voltage are shown in table 2. The code

used to produce graphs 1-3 and table 2 can be found in appendix 1. The range of zero-g voltage

given in the data sheet was from 1.485V to 1.65V [2], from table 2 we see that the measured values

of zero-g voltage for the Y and Z axis lie outside this range. By examining graphs 1-3 the error can be

estimated at +/- 0.02 V as the majority of measured values lie within this range. Graphs 4-7 can be

used to zero accelerometer one and two when using the ADS1015 ADC. The voltage at zero-g is

shown in table 3 and from graphs 4-7 we can estimate the error to be +/-0.01 V. The error in the

measured voltage at zero-g is smaller for the ADS1015 ADC than the mbed internal ADC. This is due

to the improved noise performance of the ADS1015; when taking data for graphs 1-3 using the mbed

internal ADC, 50000 averages were taken for each data point. When using the ADS1015 external

ADC, 20 averages were used for the first nine thousand data points. This led to a 50% reduction in

the noise and the last one thousand data points were taken at 3000 averages, which further reduced

the noise to approximately 25% of the original value.

y = 0.0001x + 1354.5

1335

1340

1345

1350

1355

1360

1365

1370

1375

0 2000 4000 6000 8000 10000

Voltage (mV)

N

Zeroing external ADC Z1 -axis

Taking Measurements Using mbed ADC

Once the accelerometers had been zeroed they could then be used to measure the acceleration due

to centripetal forces in the Z direction as the accelerometers were mounted with the z-axis parallel

to the direction of the centripetal acceleration. Graphs 8,9,10 and 11 show the acceleration and

angular velocity as a function of the drive voltage supplied to the motor. In Graphs 8 and 9

accelerometer 1 was at a radius of 20cm and accelerometer 2 was at a radius of 8 cm on the same

side of the rotating platform.

Graph 8. Shows the centripetal acceleration measured by accelerometers 1 and 2 at 20cm and 8 cm respectively.

y = 0.3308x2 - 0.2843x + 0.0345

y = 0.1501x2 - 0.1965x + 0.0719

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1 2 3 4

Acceleration

(ms^(-2) )

Drive Voltage (V)

Z1 and Z2 acceleration when Z1 at 20cm and Z2 at 8cm

Z1 acceleration

Z2 Acceleration

y = 1.3194x - 0.6724

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5 4

Angular Velocity (rad𝑠^(−2) )

Drive Voltage (V)

Angular Velocity V Drive voltage

Z1

Graph 9. Shows the angular velocity measured by accelerometer 1.

Graph 10. Shows the angular velocity measured by accelerometer 9.

Graph 11. Shows the angular velocity measured by the light gate .

Using equation 2 to convert the voltage output by the accelerometers to the centripetal acceleration

in 𝑚𝑠−2 graph 8 was produced. The parabola shape in graph 8 is explained by equation 3 which

shows ac is proportional to ω2, so as the drive voltage increases the angular velocity of the rotating

platform will increase linearly. This behaviour is illustrated in graphs 9-11. There are no data points

at drive voltages below 0.52V as the platform will not rotate below this voltage. The line of best fit

for the angular velocity in graphs 9-11 should pass through the origin, from equation 3 we see that

as the acceleration tends to 0 so should the angular velocity. Imperfections in the zeroing process

lead to the offset we see in graphs 9 and 10, this is why they do not pass through the origin. Graphs

9 and 10 show greater noise at lower velocities, this is partly due to the output voltage from the

accelerometers being small, so a large portion of the signal will be due to noise. When the

acceleration is 1 𝑚𝑠−2 the output voltage will be 0.0815 V +/- 0.02V using equation 2 and the error

calculated from graphs 1-3. This means as much as 25% of the signal could be down to random

noise. In addition to this there will be a position dependence of the noise as the accelerometer will

y = 1.3257x - 0.7887

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5 4

Angular Velocity (rad𝑠^(−2) )

Drive Voltage (V)

Angular Velocity V Drive voltage

Z2

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5 4

Angular Velocity (rad𝑠^(−2) )

Drive Voltage (V)

Angular Velocity V Drive voltage

LG

not remain perfectly level throughout one full rotation. Graph 11 shows large issues with the way in

which the programme measures the angular velocity using the light gate, so although the central line

displays the correct angular velocity and agrees with graphs 9 and 10 the lower line is due to the

programme not triggering at the correct point in response to the light gate. The random values are

due to the additional functions inside the programme taking much longer than the light gate and

therefore increasing the value of angular velocity measured.

Graph 12. Shows the angular velocity calculated from equation 6 using the acceleration from Z1 and Z2.

Taking Measurements Using ADS1015 ADC

y = 1.2796x - 0.5198

-1

0

1

2

3

4

5

0 0.5 1 1.5 2 2.5 3 3.5 4

Anguler Velocity (rads^-1)

Drive Voltage (V)

Angular Velocity from Z1 & Z2 V Drive Voltage

Graph 13. Shows the centripetal acceleration as a function of the drive voltage measured using the ADS1015 ADC

connected to the mbed.

Graph 14. Shows the angular velocity as a function of the drive voltage

Graph 13 shows how the centripetal acceleration from accelerometers 1 and 2 changes as the drive

voltage is increased, when both accelerometers are at a radius of 20cm from the axis of rotation.

These measurements were taken using the ADS1015 ADC to reduce the noise and hence the error.

Graph 13 and 14 show much less noise when the drive voltage is low, between 1V and 4V but as the

drive voltage is increased above 4V much more fluctuation from the line of best fit is seen. This is

because the motor is reaching its limit and is beginning to spark, therefore not all the power being

supplied to the motor is going into turning the platform. Also some of the noise could be due to

slipping of the drive belt at high angular velocities. In order to avoid this, the motor should be kept

below 4V. The accelerometer output is affected most at low accelerations due to noise, at 1 𝑚𝑠−2

the output voltage will be 0.0815 V +/- 0.005V using equation 2 and error measured from graphs 5-7

when taking 3000 averages. So the noise will account for approximately 0.6% of the signal; this is a

y = 0.2813x2 - 0.1873x - 0.0203

y = 0.2868x2 - 0.1615x + 0.0392

-1

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6

Acceleration (m𝑠^(−2) )

Drive Voltage (V)

Z1 & Z2 acceleration when Z1 & Z2 both at 20cm

Z1

Z2

y = 1.0902x - 0.1702

y = 1.086x + 0.0226

-1

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6

Angular Velocity

(rads^(-1) )

Drive Voltage (V)

Angular Velocity V Drive Voltage

Z1

Z2

tenfold reduction in the fraction of the signal due to noise, from the mbed internal ADC. Therefore

any future setup of this experiment, using accelerometers and the ARM mbed as the

microcontroller, should include the ADS1015 ADC as it improves the quality of the signal measured.

original experiment

In the original experiment the main idea is to get students to think about classical mechanics. Using

the setup on the left in figure 1.This is achieved by adding masses to the hanging mass in order to

make the brass cylinder hang vertically, then removing the hanging mass and calculating the

centripetal force necessary to return the brass cylinder to its vertical position. This is done by

measuring the radius of the side post assembly shown in figure 1, using the measuring tape on the

rotating platform. Then measure the period of rotation using the light gate and an oscilloscope. The

students will then use these measurements, to calculate the angular velocity and then the

centripetal acceleration using equations 3 and 7. This can then easily be used to calculate the

centripetal force needed to return the brass cylinder to its equilibrium position. The weight of the

hanging mass in figure 1 will be known so equation 1 can be used to calculate the centripetal force

this is shown by equation 8 (F is the centripetal force (N), 𝑎𝑔 is the acceleration due to gravity

(𝑚𝑠−2), m is the mass of the hanging mass (kg), M is the mass of the brass cylinder (kg)) .

𝑚𝑎𝑔 = 𝐹 = 𝑀𝜔2𝑟 𝐸𝑞. 8

Graph 15. Shows a graph of ω^2 v 1/r giving a gradient of mag/M.

The final part of the original centripetal force experiment is to plot a graph of ω^2 v 1/r which should

give a gradient of mag/M. Graph 15 shows the resulting plot for two sets of masses firstly m=0.0299

Kg and M=0.2086 Kg were used in series 1 giving a theoretical gradient of 1.41 𝑚𝑠−2, secondly

m=0.05 Kg and M=0.210 Kg were used in series 2 giving a theoretical gradient of 2.34 𝑚𝑠−2. The

measured gradients from graph 15 are within 5% of the theoretical values.

y = 1.4854x - 0.1066

y = 2.3899x - 0.8813

0

5

10

15

20

25

30

0 2 4 6 8 10 12

ω^2

(rad^2s^-2)

1/r (m^-1)

ω^2 v 1/r

Series1

Series2

Conclusion

The accelerometer based centripetal force experiment could be used either independently of the

original setup or as part of the current setup. Using an accelerometer based setup would allow many

more measurements to be taken in a short space of time, this would potentially be useful as part of

the aims of the original experiment are to improve data processing skills using excel. Measurements

of the acceleration between 0 and 5.5 ms-2 could be taken by varying the drive voltage to increase or

decrease the angular velocity. The measurement of the acceleration would come from the

accelerometer but the angular velocity could be measured using the accelerometer and equation 3

or by using two accelerometers and equation 6. Alternatively the light gate could be used when

connected to the mbed and the apparatus shown in figure 15, to display the angular velocity on the

LCD screen. However I think the current experiment supports first and second year modules very

well which focus on classical mechanics as well as waves and oscillations. I also think in the original

experiment having to first correct the position of the brass cylinder, then watching it return to its

vertical position when you increase the angular velocity of the rotating platform really helps build a

clear picture of what is happening. The apparatus in figure 15 could be used to display all of the

relevant data needed for the experiment, but I think this could potentially lead to miss conception as

it is quite detached. A combination of the two could be used where the student would complete the

original lab then use the apparatus shown in figure 15 to check their results. This would perhaps be

more beneficial to the students understanding than just reading results off the LCD shown in figure

15.

References

1. Mechanics: Centripetal Force- Graphical Errors Lab script. University of St Andrews.

2. Freescale Semiconductors, inc, 2008. MMA7361L, data sheet.

3. Lotters C, phd thesis, A highly symmetrical capacitive triaxial accelerometer, University of

Twente, AUG 1997

4. https://developer.mbed.org/ , 11:37 , 20/04/2015

5. Toulson R, Wilmshurst T, Fast and Effective Embedded Systems Design Applying the ARM

mbed. Elsevier , 2012

6. Kinox, Using Two Tri-Axis Accelerometers for Rotational Measurements ,AN 019, 10th January

2008.

7. Texas Instruments, 2009, ADS 1015, data sheet.

8. Multicomp ,21/12/12,NPN transistor TO-92, data sheet.