21 Rotational Motion
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Introduction
The rotary encoder is a rotational version of a motion detector. As the encoder rotates, its angular position is measured and displayed as a graph of angular position vs. time. In constructing the angular position vs. time graph, the orientation of the encoder when the LabPro first begins collecting data always serves as the origin of the coordinate system.
I. Constant Angular Velocity
A. Angular Position vs. Time Graphs
Open the file Rotation.
Collect angular position vs. time graphs for the following three motions:
- Rotating clockwise
- Rotating clockwise at a greater angular speed
- Rotating counterclockwise
To collect data, press the Collect button, wait for the encoder to begin collecting data, and then give the encoder a quick spin. If the data is clean, select Experiment/Store Latest Run. If the data is noisy, diagnose the problem and repeat the observation until the problem is solved.
Once you’ve prepared your graph for presentation, print your graph and attach it to the end of this activity.
Question: Clearly explain how the direction of rotation of the encoder can be determined from an angular position vs. time graph.
Question: Clearly explain how the angular velocity of the encoder can be determined from an angular position vs. time graph.
B. Angular Velocity vs. Time Graphs
Display a graph of angular velocity vs. time.
Question: Clearly explain how the direction of rotation of the encoder can be determined from an angular velocity vs. time graph.
C. Angular Acceleration vs. Time Graphs
Display a graph of angular acceleration vs. time.
Question: In all three trials, the angular acceleration of the encoder should be approximately constant and close to zero after you release it. Clearly explain both why the angular acceleration is constant and why its magnitude is close to zero.
II. Angular Acceleration
Display angular position, velocity, and acceleration graphs.
Hang 10 g from the end of a string wrapped around the encoder. Wrap the string so that the encoder will rotate in the positive direction, and place a small piece of tape on the end of the string so that the string won’t slip off the encoder. Press Collect, and then release the mass.
If the data is clean, select Experiment/Store Latest Run. If the data is noisy, diagnose the problem and repeat the observation until the problem is solved. Replace the 10 g with 20 g and repeat the data collection.
Once you’ve prepared your graph for presentation, print your graph and attach it to the end of this activity.
Question: Clearly explain how to determine the angular acceleration of the encoder based only on an angular position vs. time graph. Perform this analysis and record the results in the table below.
Question: Clearly explain how to determine the angular acceleration of the encoder based onl