Apparatus: The apparatus was already set up before beginning the experiment. An electric motor mounted on a surveying tripod will spin a horizontal rod mounted on a vertical rod and as the motor spins with ω, a rubber stopper attached to the horizontal rod by a string will revolve around the central shaft. As we increase ω, the stopper revolves at a larger radius and ø increases. As the stopper spins, it will strike a horizontal piece of paper on a ring stand a distance h above the ground.
Procedure: Before we derived our model for ω we needed to measure and record the distance from the ground to the horizontal rod (H), the distance from the vertical rod to the string (R), the distance from the ground to the horizontal piece of paper (h), and the length of the string to the stopper (L).
To begin deriving our model we will need to use Newtons 2nd Law on the rubber stopper.
We were able to find ø by looking at the right triangle with hypotenuse L and height being H-h.
We next spun the stopper at six different ω's using six different voltages. Each time we increased the voltage we created and measured a new h. From this data we can find ø.
Once we derived our model for ω, we found the measured value for ω by timing how long it took the stopper to make 10 revolutions around the shaft (T) and dividing it by 10 to get the time for 1 revolution.
Below is a table of our gathered data that we can use to test our model for ω and see how it compares to the measured omega. The last two columns are the values we were most interested in.
Below is a graph of measured ω vs. modeled ω.
By using a best fit line, we see the graph increases linearly and has a slope close to 1.
This tells us that our experimental data compares well with our measured data and that our modeled equation for ω is reasonable for calculating angular speed.
Conclusion: Although our model correlates well with the measured values of ω, there is still always some uncertainty in our measurements. The period T had an uncertainty of +/- .01 seconds and h had an uncertainty of +/- .5 cm.
When we plotted measured ω vs modeled ω, each different value for T and h introduced some uncertainty within each of our points. This is why the slope of our graph is not exactly one.
The final outcome of this experiment is that we were able to successfully derive an expression for ω from an apparatus that was set up in class and test it with a measured ω. It was found that as ω becomes larger, ø becomes larger.
The final outcome of this experiment is that we were able to successfully derive an expression for ω from an apparatus that was set up in class and test it with a measured ω. It was found that as ω becomes larger, ø becomes larger.
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