20 Circular Motion
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Introduction
It is quite common for objects to move along circular or semi-circular paths. Although these motions can be analyzed using a traditional xy-coordinate system, other coordinate systems, such as polar coordinates, and other sets of kinematic variables (angular variables rather than linear variables) are quite useful. In this activity, the relationships between x- and y-position and velocity to radial and tangential position and velocity, as well as angular position and velocity, will be explored.
I. Circular Motion
Open Movie and select Insert/Movie. Find the movie Circle and open it. Play the movie.
The movie shows a piece of tape with five equally-spaced dots attached to a rotating platform. The central dot is at the center of the platform. Return the movie to the first frame.
Extract position vs. time data for the outermost dot. This dot is 12 cm from the center of the platform. Scale the movie, move your coordinate system to the center of the platform, and rotate your coordinate system so that the initial angular position of the dot is zero.
A. X-Position, Y-Position and Radial Position
Create a graph of x- and y-position vs. time.
Using Data/New Calculated Column, create a new column for the radial position (the position in polar coordinates) of the dot. Add the radial position to your graph of x- and y-position vs. time and print and attach your graph to the end of the activity.
Question: Describe your graph. Do the x, y, and radial positions look as you expect?
B. X-Velocity, Y-Velocity, and Tangential Velocity
Create a graph of x- and y-velocity vs. time. Using Data/New Calculated Column, create a new column for the tangential velocity (the velocity in polar coordinates) of the dot. Add the tangential velocity to your graph and print and attach your graph to the end of the activity.
Question: Describe your graph. Do the x, y, and tangential velocities look as you expect?
C. X- Position, X-Velocity, and X-Acceleration
Create a graph of x-position, x-velocity, and x-acceleration vs. time. (Use Data/New Calculated Column, to create x-acceleration.) Print and attach your graph to the end of the activity.
Question: Describe your graph. Do the x-position, x-velocity, and x-acceleration look as you expect?
D. Angular Position, Angular Velocity, and Angular Acceleration
Create a graph of angular position, angular velocity, and angular acceleration vs. time. (You must first create these columns.) Print and attach your graph to the end of the activity.
Question: Describe your graph. Do the angular position, angular velocity, and angular acceleration look as you expect?
E. Circular Motion with Different Radius
Extract additional position vs. time data, this time for the dot 6 cm from the center.
Question: Carefully explain how the x- and y-position data for the