Impulse-Momentum activity: Jose Rodriguez: Lab partners: Kevin Tran; Kevin Nguyen: Lab Completed, 4/19/17

The purpose of this lab was to try to prove the Impulse-Momentum theorem with the data collected from several experiments.

To accomplish this goal we took a physics and mathematical type approach.  What we did was to set-up a nearly elastic collision between two carts and measured the velocity, force, and time before and after the collision for different masses per experiment; we also did one experiment with a nearly inelastic collision with the heavier of the two masses that was used for the nearly elastic collision so we could try to prove the Impulse-Momentum theorem mentioned earlier is true.  For example, we used the recorded data to calculate the area under the force vs. time graph during each trial with a tool that logger-pro has to obtain an Impulse value and then compared them to calculations for the change in momentum for the respective experiment with handwritten mathematical calculations to get a value for the change in momentum to compare and contrast the data.  The velocity was measured with a motion sensor because we could get a distance vs. time graph and then use the application tool of logger pro to get a value for our velocity which is the slope of that graph.  As for the set-up that we used, it was composed of one metal track, two metal carts, one force sensor, a digital balance, and a motion sensor.  The force sensor was calibrated and the motion sensor was confirmed to be working before we got started with the experiments.

To begin with we set up the track, weighed the two carts, and calibrated the force sensor as well as the motion sensor.  The track was a single metal track about one meter and a half long and about six inches wide; one of the carts had a spring attached to its front side and was attached in a horizontal manner to metal rods and clamps, and the other had the force sensor firmly attached to the roof of it with the actual force sensor facing the collision site to measure the collision force per each experiment.  As for the motion sensor it was facing the rear of the cart with the force sensor attached to it, about thirty centimeters away.  Then we opened up the logger pro computer application, gave the cart with a force sensor on its roof a push towards the one secured, measured the force, distance, and time per respective experiment so we could gather data necessary for the completion of the force vs. time graph as well as the distance vs. time graph for each experiment.  Importantly, the nearly inelastic experiment was done differently then the first two because we took of the cart the was attached with the rods and clamps then placed a clamped piece of wood with clay on its front so the cart with the force sensor could hit the wood and get stuck when they collide.  Also, the tip of the force sensor was changed from a rubber stopper type tip to one that had a sharp point so it can get stuck the impact site to get an inelastic type collision.  For experiment one we used the mass of the cart only, and for experiment two and three we added five-hundred kilograms to the top on the cart with the force sensor on it. Next, for the calculated values of the impulse per each trail we used a tool the logger pro application program has that let us get a value for the area under the graph ( or integral ) that is the value for the impulse for each experiment.  Lastly, the calculations for the change in momentum was done by hand because we had the mass of the cart and the value for the velocities before and after the collision for each experiment.

This is an image of the set-up for the first two experiments of the nearly elastic collisions.  Notice the way that the cart was attached horizontally with the rods and the clamps.  Also, note that the professor was calibrating the force sensor.

This image shows the third experiment for the nearly inelastic collision from the rear.  Note the clay attached to the piece of wood instead of the horizontal cart with the rubber type tip.

This is the image taken of the graphs of the distance vs. time on top and the force vs. time graph on the bottom for experiment one.

This is the image taken of the graphs of the distance vs. time on top and the force vs. time graph on the bottom for experiment two.

 

    This is the image taken of the graphs of the distance vs. time on top and the force vs. time graph on the bottom for experiment three.  Note that the force vs. time graph looks different after the main area under the graph in contrast to experiment one and two.  I think this may be due to the tip of the nail on the cart getting stuck to the wood or the clay on its way back after the impact.

This is an image of the calculations for change in momentum of each experiment and the absolute difference between the Impulse and change in momentum.

In conclusion, the experimental values that we calculated were very similar in value hence the whole lab proved to show evidence that the Impulse and Momentum theorem is true.  Of course, I do believe in the theorem because smarter men discovered it so regardless of the errors that we found in our total experiment does not deflect me from believing the theorem.  Although, our errors were such a low value that I believe we did the experiment adequately well. The absolute difference for experiments one through three: 0.0116 N*s; 0.0055 N*s; 0.0182 N*s.  As for the reason(s) for errors, I think one was that we didn't weigh the cart with the force sensor on top of it so that through the calculations of for change in momentum.  That error would definitely cause a difference in the values of Impulse and Momentum.  Otherwise, the force sensor may be a cause for error because it may of slightly malfunctioned during the trials.  But, that error would be hard to prove.  Interestingly, the force vs. time graph for the last experiment is different I believe because the nail got stuck to the wood or the clay so it pulled back on the force sensor causing a negative force that is seen after the main total force area of the experiment.  Lastly, even though the values for Impulse and change in Momentum were not the same I think the theorem clearly presented itself because of the close precision between values.

Magnetic Potential Energy: Jose Rodriguez: Lab Partners: Kevin Tran; Kevin Nguyen: Lab completed: 4/17/17

The goal for this experiment was to prove that energy is conserved, and in the process show that the potential energy of a system is due to some force before the existence of it.

To try to prove this goal, we took the approach that says for any system that has non-constant potential energy the potential energy is caused by an interaction force (F).  Hence, we used a glider with a magnet attached to one end (on an air track) and had it glide towards a magnet at one end of the track at various angles and recorded the distance (r) between the magnets when the glider stopped by itself so we could get enough data to make a graph that gave us a relationship between the force (F) and the distance (r).  The force in this case was calculated with gravitational potential energy (mgh), since we assumed that this was the only force acting on the glider on its way towards one end of the track.  To get the relationship we used a power fit curve that calculated the slope values for two variables that would complete the formula for our assumed potential energy of the system.  Last, to test that our formula was correct we did an experiment where we gave the cart a gentle push and measured its kinetic energy with the help of a motion sensor that recorded the distance and time of the cart during the trial so we could obtain the velocity of the cart.  That data allowed use to get a value for kinetic energy that had to match the simultaneously recorded values for potential energy and total energy of the system.  The potential energy of the system was calculated with the use of our formula the was obtained earlier in the experiment, and the use of the motion sensor that calculated the distance (r) that we had to plug into our formula for potential energy.

To begin this experiment, we had to level the track that the glider would glide on and measure the mass of the glider.  To level the track, we used a program on Kevin's iphone called "bubble level" and to measure the mass we used a digital balance.  Next, we did several trials that involved tilting the track and turning on the power source of the air track (so the glider would glide) and let the glider travel towards the end of the track until it stopped by itself so we could measure the distance between the magnet ends and the angle of the track for further use.  The calculations for the gravitational potential energy of each trial were then calculated with the formula (mgh) were "h" was the value of sin(angle) and entered into loggerpro so we could make a graph of the force per each trial vs. the distance (r) between the magnets per each trial.  Note that the angle per each trial was also measured with an application on Kevin's iphone.  After that, the slope of the graph that we had just made allowed us to obtain a power fit formula for the potential energy of the system in relationship to the distance (r) per each trial.  Lastly, to test the formula we did another experiment in which we calculated the kinetic energy of the glider by giving it a gentle push towards the magnet end of the track with the use of logger pro and a motion sensor and compared it to the potential energy and the total energy of the system during that experiment.  The potential energy graph was given the formula that involved the distance (r) which the motion sensor measured during the trial to complete the graph, and the total energy graph was given the formula of total energy= kinetic energy+ potential energy.

     
This is an image of the air glider and its' track. Note the motion detector at the same end of the track as the magnet.

This is another image of the track set-up.

This is an image of the Force vs. radius graph that we used to get the unknowns for our power law formula for the assumed potential energy formula.  Note, the values for A and B on the slope box were the ones we used for our calculations.

This is the power law formula format that we tried to get with our data: F=Ar^n.

This is an image of one example calculation for the gravitational potential energy and the integration to obtain our potential energy formula.  Note the mass of the glider.

This is an image for the proof that our formula for potential energy was correct because the graphs show that the energy of the system was conserved during the experiment.  Hence, the kinetic energy all turned into potential energy when the glider stopped and the total energy (in blue) was conserved during the total experiment. Note that the distance (r) between the magnets changed, but that both of the graphs still showed the energy was conserved leading towards the proof that our formula for potential energy was correct.

In conclusion, we did gather enough energy to show that potential energy is a cause of some force before the measurable value of potential energy.  For example, the graphs showed that the energies were conserved because once the kinetic energy went to zero then the potential energy increased to the last value of the kinetic energy; also, the total energy of the system (that is seen through the graph) was at a constant total value of energy throughout the experiment.  As far as errors for this experiment, not many were noticed by me because my interpretation of the graph that displayed the three energies is that the total energy that was in the system was conserved throughout the experiment. Although, I do believe frictional force was involved during the experiment (but I can't prove it) and that the measurements for the distance (r) during the entire experiment were slightly off so that caused the experiment to have some incorrect results that I can't explain with the given results.  The reason I think there was frictional force is because the air track that we used was very old so I think there were areas in the track with less air flow that caused some friction; and the reason I think there were distance measurement errors is because we used a simple ruler that is not 100% accurate.  Lastly, even though there were likely errors we were still able to see a clear relationship that lead me to conclude that we did prove there is a conservation of energy for a system.

Work and kinetic energy theorem: Jose Rodriguez: Lab completed: 4/10/17: Lab partners: Philip, John.

The focus of this lab was to try to show that work is equal to kinetic energy of an object during acceleration due to a force.

To try to prove this relationship we did several experiments and recorded data.  The experiments were based on capturing the values of force vs. distance of a cart that rides on a metal platform.  Then, the values for the forces and the displacement were entered into LoggerPro so we could make a graph that allowed us to integrate the area under the slope of the graph that in return gave us the value for the work done at any given point of the graph.  With this information, we then made a graph of kinetic energy vs. position and superimposed it onto the force vs. position graph and used a tool that allowed us to integrated both graphs at the same time to see the respective values at a specific point.  Lastly, the main techniques that were used for this lab were physics, a computer program, and some sensors.

To begin with, we had to set up a metal ramp that allowed a small cart to travel a short distance while being pulled by the tension of a string tied to hanging weight.  The distance and time the cart took for this displacement was captured with the use of a motion sensor, and the force was captured with a force sensor that was connected to the cart which all was recorded by a computer with the application logger pro.  Once the trial was completed, we used the all that data to make a graph of force vs. distance and imposed one of kinetic energy vs. position so we could use a tool that allowed us to integrate the area in between both graph so we could see the values for work and kinetic energy at the same time during any point on the graphs.  Ultimately, to confirm our findings we did the same type of experiment with the use of a spring instead of string to supply the force measured during the displacement of the cart.  We locked the spring in between the force sensor and the cart during displacement and repeated the same process that resulted in similar result.

This is an image of the cart and the hanging mass.  Notice the sensors that are all connected to the computer so we could record data.

This image shows the initial recordings of the experiment of the cart with the hanging mass.  Notice that we needed the time in all the graphs so we could link all of them together.

This image already shows the slopes of the force and velocity graphs are similar.  For instance force slope value is .389 and  velocity is .314; the absolute is 0.075.

This image shows the superimposed graphs of force and kinetic energy for the first part of the experiment.  Notice that work .1705 n*m is very close to kinetic energy 0.155 J.  The absolute difference is only .0155.

This image shows the graphs for the part of the experiment that involved the spring as the intermediate.  Again, notice the the slope values of force and kinetic energy are very close to one another.  The absolute difference is 0.0108.

In conclusion, the experiments did prove to show that there is a definite similarity between work and kinetic energy of an object during displacement. Although the values did not match, they were very close in value.  One reason that we didn't get a 100% match may have been because the motion sensor was not positioned the way it should have been so it didn't capture the distance traveled properly.  This error will throw off the kinetic energy because it measures velocity which is dependent of displacement. Another reason may be because the force sensor was not properly calibrated.  My lab partner calibrated it a way that was not recommended so the force sensor never read the exact force that is showed have sensed.  In return, the force values were never exact so work and kinetic energy were never going to be equal.  Although, the similarity and theorem were proven in my eyes because the values had such a small absolute error as mentioned in the image descriptions of the graphs.

Work and Power: Jose Rodriguez: Lab Partners: Kevin Tran; Kevin Nguyen: Lab completed: 4/5/17

The purpose of this lab was to find relationships between power and energy by completing several experiments.

The way we approached this lab was to conduct three experiments that would give us the needed variables to calculate work and energy the was used during the experiments.  For example, we went outside of the classroom to walk up a flight of stairs, run up a flight of stairs, and pull a weighted backpack up a certain height.  With these steps taken, we measured the height of the flight of stairs, the time intervals during all trials, the mass of the backpack, and the angle of the stairs so we could use the concept of work and energy to calculate work and power output during these trials.  The mathematical calculations that were used were simply work=mgh, power=energy/time, and velocity=distance/time. The data that was recorded during this lab was used in conjunction with these mentioned formulas to calculate the work and power that we used during each trial.

To begin with, we went outside of the classroom to an area that had stairs and an upper level that we could use to set up a rig with a pulley and a thin rope that we could use to pull up the backpacks.  Then, the professor set up the rig and we began to pull the backpacks up one at a time.  There were three backpacks that were each lifted one time all the way to the top of the rig, and the time interval was taken for later calculations.  Also, the height of the flight of stairs was taken by measuring the height of one stair and then multiplied by the total amount of stairs.  As for the angle, it was given to us by the professor.  Next, the flight of stairs were climbed once walking and the other time running per the needs of the experiment; the time interval was recorded for later calculations.  Last, we went into the classroom to calculate the work and power values that were used during each trial as well as other calculations that were asked of us.

This image shows the professor securing the backpacks to the rig that he set up on the upper level. The stairs that were climbed are on the left of the picture.

This is an image of the recorded data for the stairs and the backpacks. Note the time intervals per each trial.

This image shows the calculations for the work and power used during each of the stairs trial.

This image shows the calculations for the work and power used during one backpack trial.

 This is the calculation for part B of the conclusion questions.

This is the calculation for the conclusion questions part C.

These are the calculations for part D.

In conclusion, we were able to use the data that we recorded during the experiment trials to obtain a work and power value.  The simple experiment was completed with the help of physics knowledge and mathematics, yet again proving that these tools prove valuable in our world.  As far as error for this lab experiment, there may have been some slight error because we timed our time intervals with a simple wrist watch and measured the height of one step of the stairs with a meter stick so none of these objects are as precise as tools as others that were not available to us to measure these variables. But, I think that with the given tools the approximate values for work and power probably had a ten percent standard deviation.  Also, the kinetic energy was not taken into account for the calculations of work and power during the trails because it's not needed per the physic's skills to calculate work or power during these trials.  As for the error this introduces, I think there was not much of an error introduced because the calculations for work and power didn't include kinetic energy at all. Overall, the link between energy and power was used in order to obtain the asked for calculations so I believe we did complete the task of finding some relationship between work and power.  Lastly, I was not able to correct the upside down photos so sorry about the upside down view.

Centripetal force with a motor: Jose Rodriguez: Lab partners: Kevin Tran; Kevin Nguyen: Lab completed: 4/5/17

The purpose of this experiment was to find a relationship between the angle of a swinging object on a pendulum and the respective angular speed.

There are several measurements that we had to record in order to come to an educated conclusion for the relationship that we wanted to establish.  First, we had to record the dimensions of the apparatus that we used so we could calculate the angle from its' central support to the line of string that was connected to the swinging object. For instance,we measured the height of the object from the floor, the radius of the extended arm, and length of the string that were all part of the apparatus so we could the formula angle= arccos(H-h/L) to calculate the angle per each trial.  Second, we had to record approximately how much time the object would take to pass the same point ten times so we could calculate the angular speed by dividing 20(3.1459)/delta time of each trial to get the Omega for each trial.  Last, we used the force diagram of the hanging object to get a formula that relates omega and angle.

To start this experiment, we had to measure the apparatus so we could have data to make certain calculations.  We measured the height, the radius of the arm that extended out away from the shaft, and the length of the string and recorded the measurements.  Then, the professor flipped the switch to the power source of the apparatus and the object began to swing in circles as we recorded the time it took the object to revolve around the same point ten times so we could calculate the angular speed per each trail.  Once everyone had taken the needed measurements, the professor used a simple apparatus that indicated where the height of the object was per each trial so we could record the height of the object for each trial and use the information for the calculations for the angle per each trial.  Last, we used the collected data to calculate the angle and omega and also to make a graph of the calculated omega vs. visualized omega.

This image shows the apparatus that was used for the experiment.  It is built with a tri-pod stand, an electric green motor with a metal rod sticking out of it, a horizontal meter stick, and a hanging black object connected to a string that is connected to the meter stick.

This is a closer image of the apparatus.

This image shows the force diagram for the experimental object and the derived formula for the relationship between omega and the angle on the top left hand side of the paper.

This is an image that illustrates the data that was recorded for the experimental trials and all the calculations that were used to obtain needed variables.

This is an image of the data for the last two trials.

This image shows the data the was used for the graph of the calculated angular speed vs. the visualized angular speed.  Notice that the graph has almost 100% correlation.

This is a further view of the graph just mentioned.

In conclusion, we did find some relationship between the angle and the angular speed of the swinging object.  For instance, what we visualized vs. what we calculated with mathematical formulas and physic's knowledge did create a graph with almost 100% in correlation between the two which leads me to think that the approach we took to find the relationship was successful.  The difference in the two angular speeds could have been due to several reasons. For example, the values for the rotations of the object in relationship to the metal frame that was used were calculated with our vision and the use of a wrist watch that I pressed for each trial's time interval.  So there is likely some calculation error for the time interval that translated down the physical calculations.  Also, the way we measured little (h) for each trial was not accurate at all because we just eyeballed the height every trial and measured it with an old meter stick that had worn out number units that had hard to see values.  Lastly, the apparatus itself was not precise for each trial because it was built unstable.  For instance, the motor was taped on to the tri-pod and the me tri-pod itself was not completely vertical for each trial which also lead to errors in the mathematical calculations.  Hence, there were many reasons why the calculated values for the angular speeds were different but I think we did show that there is a relationship between the two because the values were close to one another and because the graph gave the value of 0.9935.

Centripetal Acceleration vs. Angular Frequency: Jose Rodriguez; Kevin Tran; Kevin Nguyen: Lab completed 3/29/2017

The main focus of this experiment was to determine the relationship between centripetal force and angular speed.

The measurements that we recorded for this experiment were done so in hopes of finding the relationship mentioned.  More specific, we wanted to measure how long it takes a point on a disk to make a number of rotations in a known time interval and the Centripetal acceleration it would experience during each trial.  Physics says, that any force equals mass times acceleration so then the centripetal force must equal mass times acceleration.  Thus we measured the mass of our object with a digital scale and the acceleration by using the rotational angular acceleration physics formula that says radius times omega squared is equal to angular acceleration. Accordingly, we measured the force a mass would experience during radius of our object for each trial with a ruler.  As for the omega, we had to record the time interval per trial and the number of revolution per that same trial to convert that information into rads per second by using mathematical knowledge.  Lastly, we varied omega by changing the time intervals for several trials during the experiment to calculate the force per each trial.

This experiment began with us gathering around an apparatus that was set-up by the professor.  The apparatus was a wooden wheel that spins in a circular motion supported by makeshift desk wheels and powered by an electrical scooter motor to create the spinning action.  Also, a photogate sensor (which was connected to logger pro) was set-up to measure how fast a piece of tape that was attached to end of the wheel rotated in a timed interval. Once that was in place, a mass was attached to a string and a wireless force sensor (which was attached to the center of the spinning disk) and the wheel was allowed to spin.  Then, the power supply was adjusted and the disk spun until it had a fairly constant speed before the force was measured for an interval of ten rotations with the photogate sensor.  Since we had to vary variables independently, we recorded three good trials per each variable change.  For example, the mass was simply varied be changing the object that was used and the radius was varied by changing the length of the string per its respective trial.  As for omega, it was varied by adjusting the dial to the power supply so that the time intervals of the ten rotations would be faster with increased power or slower with decreased power to the electrical scooter motor.  The force and time interval for each respective trial was recorded by logger pro with the help of the professor who counted the rotations with a graph that logger pro illustrated per ten rotations.  Lastly, we entered the information into logger pro to create graphs and linear trend lines that illustrated the slope per each graph that helped us conclude our findings when two variables were left constant.  For instance, we made one graph of force vs. mass that gave us a slope almost equal to the radius times omega squared, another for force vs. radius that gave us a slope value almost equal to the mass times omega squared, another for force vs. omega squared that gave us a slope almost equal to the mass times the radius, and two more that gave us values of slopes almost equal to radius and mass respectively.

This is an image of the spinning disk apparatus that was used to record data.  Notice the photogate sensor to the right of the image and the piece of white tape that were used to record the time per each rotation.

This is an image of the display that logger pro allowed us to view that recorded the force and the time per each trial.  Each apex on the line graph is equal to one rotation, so that's how the professor was able to isolate only ten rotations for our experimental values.

Table #1.

Data when only the mass was changing after 10 rotations
Variables	trial #1	trial #2	trial #3
mass (kg)	0.10	0.05	0.30
radius (m)	0.47	0.47	0.47
power supply (P)	3.00	3.00	3.00
start time(s)	2.68	1.54	2.35
end time (s)	17.00	14.97	16.46
force(N)	1.05	0.57	2.80
time interval (s)	14.32	13.43	14.11

Table #2

Data when only the radius was changing after 10 rotations
Variables	trial #1	trial #2	trial #3
mass (kg)	0.20	0.20	0.20
radius (m)	0.23	0.29	0.47
power supply (P)	3.00	3.00	3.00
start time(s)	1.43	1.73	1.57
end time (s)	14.77	14.88	15.60
force(N)	1.20	1.47	1.48
time interval (s)	13.34	13.15	14.03

Table #3

Data when only Omega was changing after 10 rotations
Variables	trial #1	trial #2	trial #3
mass (kg)	0.3	0.3	0.3
radius (m)	0.4699	0.4699	0.4699
power supply (P)	3.5	3.8	4.1
start time(s)	1.24	1.13	1.46
end time (s)	11.48	10.74	10.6
force(N)	5.39	5.94	6.43
time interval (s)	10.24	9.61	9.14

Table #4

Calculations of 10 rotations into Omega (rad/sec)

10 rotations = 10 revolutions: 2(3.14159) rad = 1 revolution: 10 revolutions = 20(3.14159) rad

  

Table #5

calculations for Omega and Omega squared taken from the Data chart for when omega was changing
trial #1 (rad/sec)	trial #2 (rad/sec)	trial #3 (rad/sec)	omega squared (rad/sec)
2(3.14159)/10.24=6.14	2(3.14159)/9.61=6.54	2(3.14159)/9.14=6.87	trail #1 = 6.14x6.14=37.7
		Trial #3 omega squared= 47.2	trail #2 = 42.8

Formula one.

Force toward the center = ma = r(m)(omega squared)

 Graph #1

This is a graph of force vs. radius(omega squared) that was taken from the values of data in table #3 above that has the power source value changing only.  The slope is supposed to be equal to the mass of the object that was calculated as .3 kg.  The value of this slope is 0.2292.

Graph #2

This is a graph of force vs. mass(omega squared).  Note that the image says mass(radius squared) but that is wrong.  These values were also taken from table #3.  Its slope is supposed to give us a value of the radius of the object from the center of the spinning disk.  The illustrated value of the slope in this image is 0.3667, and our measured radius was .4699 meters.

  

Graph #3

  This graph illustrates force vs. omega squared and its slope is supposed to be the value of the mass times the radius.  The values were taken from table #3.  The slope value is 0.1078, and from the table values it should be 0.1410 kg(meters squared).

graph #4

This is the graph for when the mass of the object changed.  The slope is supposed to be the value equal to the radius(omega squared), and the illustrated value is 8.869. These values were taken from table #1 and the calculated value should of been 9.072. 

In conclusion, we tried to prove that the centripetal acceleration is equal to the mass*(radius)*(omega squared) by completing several experimental trials while changing one variable at a time.  The graphs that were created with the respective data displayed slope values that were close to the expected values, but the slope values were never equal to the intended and calculated values.  For instance, graph #1 has a slope that is supposed to be equal to the mass of the object tied to the end of the string when radius was supposed to be the only variable changing.  Yet, the absolute difference was .07 kg. Also, graph #2 was supposed to have a slope representing the value of the radius of our tied object but it had an absolute difference .10 meters.  Respectively, graph #3 and #4 had an absolute difference of .03 kg*m and .2 m*rad/sec^2.  So the experiment did not give us exact values for the intended variables, but they were close.  The inaccuracy can probably be due to several factors.  One may be the that the length of the string could have been calculated with some error because it was measured with a simple ruler with a simple glance.  That simple error may have carried throughout the calculations that we did for this lab and resulted in an even larger numerical value error.  Another factor is that the power source that supplied energy to the scooter motor was not calibrated in a manner that we knew it was accurate in its gauge reading of energy output, so that could of resulted in the calculations that we did for omega to be wrong.  For example, graph #2 represents force vs. mass*omega squared with a slope that is supposed to be equal to the radius (but is not) with an absolute difference of only two tenths of a second.  Lastly, the apparatus that spun around had very unbalanced motion due to the makeshift engineering that most likely was the main cause of the faulty conclusions.  It had wheels the supplied the spinning possibilities to the apparatus that seemed close to breaking that must of supplied resistance to the system, in return affecting the calculations significantly very likely by affecting the omega calculations just like the uncertain power supply connected to the system.  To summarize the experimental values were not exactly the correct values that they should have been, but I believe that the experiment did prove that the centripetal acceleration is a value that can be calculated with the above mentioned formula of radius*mass*omega squared.