I-Shou Lin, Kirk Paderes, Jorge Avalos
4/ 3/17
To determine and observe the relationship between the angle and angular velocity
In the apparatus of this lab, the mass revolves around the central shaft at some angular velocity ω making an angle θ with an imaginary vertical line straight down from the pivot at which the axis sags. As the angular velocity increases or decreases, the angle also changes. With enough data points relating the values of h at a variety of values of ω, we can extrapolate the relationship between h and θ and hence the relationship between θ and ω. This result can then be compared to the theoretical result.
We just watched the apparatus operate and took data values for angular velocity and h.
Data Table
L ( meters)
|
H ( meters)
|
h ( meters)
|
Δt ( seconds)
|
R ( meters)
|
1.63
|
1.81
|
0.817
|
0.81
|
|
1.63
|
1.81
|
0.385
|
3.29
|
0.81
|
1.63
|
1.81
|
0.623
|
2.8
|
0.81
|
1.63
|
1.81
|
0.935
|
2.28
|
0.81
|
1.63
|
1.81
|
1.15
|
1.946
|
0.81
|
1.63
|
1.81
|
1334
|
1.64
|
0.81
|
1.63
|
1.81
|
1.422
|
1.39
|
0.81
|
Calculated Results
Angular Velocity
|
Angle θ
|
Total Distance ( meters)
|
2.4498985174
|
52.4681425
|
2.12529283
|
1.843530386
|
29.0456538
|
1.60137539
|
2.187672252
|
43.262551
|
1.92710832
|
2.65490186
|
57.5332679
|
2.18523634
|
3.127021158
|
66.4985045
|
2.30479096
|
3.680846363
|
73.0207988
|
2.36894965
|
4.08764462
|
76.2292998
|
2.3931475
|
The graph above depicts the relationship between angular velocity and angle the apparatus made with the vertical. As the apparatus spins at a higher angular velocity, the radius would get bigger and the angle would increase. But, how fast does it increase, and does it increase at a linear or some power rate is what the graph can show. The equation of the graph: y= 0.1146*x^0.7967 transmits the mathematical relationship between the angle and angular velocity of the apparatus. The equation was obtained through format trend-line on Microsoft excel.
In conclusion, the relationship for the angle and angular velocity based on the theoretical derivations showed a directly proportional power curve. The entire course of the experiment was data collection. The angular velocity was calculated through timing how many revolutions per amount of time elapsed, and the angle was derived through measuring the height h of the ring stand. There might be some uncertainty associated with the height because the apparatus probably didn't just strike the very tip of the paper all the time. It might have struck the lower part. This would've introduced a source of error into the angle calculations and hence the angular velocity and total distance results. Overall, the lab produced good measurable results.
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