Lab 8: Centripetal Acceleration vs Angular Frequency

←               Centripetal Acceleration vs. Angular Frequency 
                     Ian Lin, Kirk Paderes, and Jorge Avalos
                                         3/27/17 and 3/29/17 

To determine the relationship between centripetal force and angular speed with the variables of mass, radius, and angular speed

There are many factors in play on a rotating surface. All of these factors are related by the equation of F= m*r*w^2, and the force is the centripetal force that points toward the center of the circular surface. We investigate the effect of changing each of one of these variables while holding the other two constant and then graph the results. This is done experimentally by adding mass onto the disk, adjusting the radial distance, and changing the angular speed through adjusting the voltage on the power supply.

The students' role in this lab was to take and record data while the professor experimented on each of the variables.

( top-side view of the circular disk)


Data Table

Power Supply	Mass (kg)	Radius ( meters)	Force ( newton)	Δ T ( seconds)
3	0.3	0.47	1.31	20.52
3	0.2	0.47	0.8031	20.89
3	0.1	0.47	0.4332	21.35
3	0.05	0.47	0.2792	25.41
3	0.2	0.548	1.66	17.04
3	0.2	0.548	1.651	14.63
3	0.2	0.548	0.873	14.43
3.4	0.2	0.548	4.304	8.8
3.8	0.2	0.548	6.4	7.27
4.2	0.2	0.548	10.36	5.86

Calculated Results 

ω^2	rω^2	mω^2
9.375728525	4.406592407	2.812718558
9.046547269	4.251877216	1.809309454
8.660919021	4.07063194	0.8660919021
6.114351569	2.873745238	0.3057175785
13.59629428	7.450769264	2.719258855
18.44467828	10.1076837	3.688935656
18.9595085	10.38981066	3.791901699
50.97936158	27.93669014	10.19587232
74.69489395	40.93280188	14.93897879
114.9646985	63.00065478	22.9929397

ω^2= (2π/t)^2= (2π/2.052)^2= 9.375728525 /s^2
rω^2= 0.47 m* 9.375728525/s^2= 4.406592407 m/s^2
mω^2= 0.3 kg * 9.375728525= 2.812718558 kg/s^2

These three graphs above represents the relationship between centripetal force and one of the three variables of mass, radius, or angular velocity while holding the other two variables constant. It's with these graphs of comparing the centripetal force against one variable in question that allows us to examine the effect that the mass, radius, or angular velocity has on the force. The slopes for these three graphs in fact depict the the product of the other two variables not in question. For the graph of the force vs mass, the slope of the graph should be the product of angular velocity squared times the radius. For the graph of the force vs the radius, the slope of the graph should be mass times angular velocity squared, and for the graph of the force vs. angular velocity squared, the slope of the graph should be mass times radius.


In conclusion, the examination of each of the variables' effect on the centripetal force were graphically well, although the graph of the force vs. radius only had two data points. That's the minimum required for a linear fit. But, the main purpose of determining the relationship between centripetal force and angular speed produced a graph with 6 data points that produced a linear fit with a slope of 0.0904 which is very close to the theoretical result of 0.1096. However, there're several sources of error/uncertainty present such as the force sensor on the rotating disk and the assumption of a constant angular velocity. The force sensor's recordings could affect the value of the recorded centripetal force and therefore the theoretical slope for the graphs, and the angular velocity might not be constant due to the workings of the power supply which could in turn deviate the data from the theoretical results.