Unifrom Centripetal Motion Grapher

In this section you will analyze the results you observed from running the Uniform Centripetal Motion Simulation by plotting the points of centripetal acceleration versus the radius.

Below is a graph of a the centripetal acceleration simulation run at a velocity of 6.5, and how much the acceleration changed as the radius was changed. As you can see, the curve starts out slowly, with many points far from each other, and then the points start to come together and the graph starts from a high centripetal acceleration to a lower centripetal acceleration based on the radius of the object travelling in circular motion.

If you would like to see the full code for plotting the centripetal acceleration and radius graph, click the Display Code button below:

# import required libraries import matplotlib.pyplot as plt import numpy as np def doafit(radius, centripetal_acceleration, order): # initialize layout fig, ax = plt.subplots(figsize = (9,9)) # add scatterplot ax.scatter(radius, centripetal_acceleration, s=60, alpha=0.7, edgecolors="k") params = np.polyfit(radius, centripetal_acceleration, deg=order) ta = np.array(radius) xseq = np.linspace(ta.min(), ta.max(), num=100) # plot regression line ff = 0. for i in range(len(params)): ff += params[i]*np.power(xseq,order- i) ax.plot(xseq, ff, color="k", lw=2.5) # axis and title plot labelling ax.set(xlabel="Radius", ylabel="Centripetal Acceleration", title="Uniform Centripetal Motion") ax.grid() return plt # centripetal_acceleration and radius inputs centripetal_acceleration = [28.3, 17.73, 13.66, 9.74, 7.57, 6.53, 5.74, 5.12, 4.62, 4.21, 3.75, 3.47, 3.19, 3.03, 2.85, 2.63, 2.46, 2.32, 2.23, 2.12] radius = [1.5, 2.4, 3.1, 4.4, 5.6, 6.5, 7.4, 8.3, 9.2, 10.1, 11.3, 12.2, 13.3, 14.0, 15.1, 16.1, 17.2, 18.3, 19.0, 20.0] deg = 2 doafit(radius, centripetal_acceleration, deg)

Here is a code editor so that you can input your centripetal acceleration and radius data points based on your observations made using the Uniform Centripetal Motion simulation.

This is how the centripetal acceleration and radius inputs should look like:

centripetal_acceleration = [28.3, 17.73, 13.66, 9.74, 7.57, 6.53, 5.74, 5.12, 4.62, 4.21, 3.75, 3.47, 3.19, 3.03, 2.85, 2.63, 2.46, 2.32, 2.23, 2.12]

radius = [1.5, 2.4, 3.1, 4.4, 5.6, 6.5, 7.4, 8.3, 9.2, 10.1, 11.3, 12.2, 13.3, 14.0, 15.1, 16.1, 17.2, 18.3, 19.0, 20.0]

order = 1 means linear fit (i.e. polynomial of degree 1)

order = 2 means quadratic fit (i.e. polynomial of degree 2)

doafit is what generates a fit line or curve based on the time and height inputs.

In the uniform centripetal motion simulation, graph the force and velocity. What do you notice in the shape of the curve? is it linear? parabolic?

Do you notice any similarites or differences in your graph compared with the graph above?

Record your observations in the Centripetal Motion worksheet provided in the worksheet section of the Exercises Page.

centripetal_acceleration = [] radius = [] order = 1 doafit(centripetal_acceleration, radius, order )

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