Kinematics of Circular Motion

Simulation

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Purpose:

• to analyze the kinematics of uniform circular motion using an Interactive Physics^TM simulation

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Discussion:

In this simulation, you will set up and study an example of uniform circular motion and plot graphs of position vs. time, velocity vs. time, and acceleration vs. time. I recommend that you use Graphical Analysis^TM to draw your graphs, although you can always graph them by hand if you choose.

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Setup:

Interactive Physics^TM:

1. Ask your instructor whether you will be analyzing position, velocity, or acceleration (or all three!) in this simulation.
2. Open the Interactive Physics^TM program.
3. Go to the Workspace submenu of the View menu, and check "Rulers" and "X,Y axes"
4. In the World menu:
   1. Set Gravity to "None"
   2. Set Accuracy to "Accurate"
5. Create a new object, and place it at the point (1, 0).
6. Create a bar to connect the center of this object to the point (0, 0).
7. Open the Properties Window of the object. Be sure that x = 1.000 m and y = 0.000 m. Set v_y = 1.00 m/s
8. Create a timer (from the Measure menu).
9. Create a meter to measure the position, velocity, or acceleration (did you forget to ask?) of your object. You want a digital readout. Select "All" from the submenu.
10. Define vectors to display the velocity and acceleration (Define menu) of the object.
11. Run the simulation. You should get circular motion, although it may be a little on the jerky side - that's ok. You have an object with a constant speed of 1.0 m/s moving in a circle of radius 1.0 meter - about how long should it take the object to go around once (it's period)? If that's ok, move on.

A screen shot of the simulation	The Properties Window

Graphical Analysis^TM:

1. Open the Graphical Analysis^TM program.
2. Go to Preferences (in the File menu) and set angle measure to "Radians".
3. Make a new column (in the Data menu) and label the three columns t (in sec), x (or v_x or a_x), and y (or v_y or a_y).

   A sample data table

4. Open a new graph (Graph menu), and make one graph an x vs. t graph, the other graphs y vs. t.

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Procedure:

1. Reset the simulation and record t, x, and y (or t and whatever) in your data table (in Graphical Analysis, as if I need to say it...).
2. Now, run the simulation for a short time. Use the movie controls and the timer to move the simulation to 0.2 seconds. Record t, x, and y in the data table.
3. Continue, recording t, x, and y every 0.2 seconds until one "orbit" is completed.

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Analysis & Conclusions:

1. Use "Automatic Curve Fit" (in the Analyze menu) to get a best-fit curve and equation for your data. You should be able to figure out which model to use. (Note: Did you get some really strange coefficients in your best-fit equation? If so, did you forget to switch from degrees to radians?)
2. Compare your results with the results of the other lab groups who have analyzed some other kinematical quantity.
3. Write a short summary of your results. Be sure to note the directions of the velocity and acceleration vectors.