THEORY: Conservation of angular momentum requires that the angular momentum of an object be conserved if no external torque acts on it. Angular momentum is given by
and conservation of angular momentum is given by
where l is the angular momentum (in Newton meters), I is the moment of inertia (I = MR² for a point mass and is expressed in kg m²), and w is the angular velocity (given in radians/sec).
Conservation of energy requires that the total energy an object has at one time is equal to its total energy at another, if no energy is gained or lost. Energy may change forms but total energy is conserved. Rotational kinetic energy is given by
EQUIPMENT: Computer, and VideoPoint software.
PROCEDURE: There are two video files from which to chose. From the "PRU" subdirectory chose one of the following Pru043 or Pru044. With the VideoPoint software mark the position of the rotating object as it moves as demonstrated in the "Instructions for using VideoPoint". Record the mass of the puck listed on the first frame of the video. Mark the position of the puck. Calibrate the video. Relocate the origin of the coordinate axis to coincide with the hole in the table about which the puck revolves. Plotting position and radius as functions of time will generate the angular velocity and radius in the data table. For the Pru043 video record the time, angular speed, and radius of path of the puck for ever 0.5 sec for the intervals from 3.5 to 7.0 sec. For the Pru044 video record the same data for the intervals between 4.0 and 12.0 sec at 0.5 sec intervals. This data can be used to calculate the moment of inertia, angular momentum, and rotational kinetic energy of the puck as it spirals inward, when the string pulls the puck toward the center of the table.
A step-by-step procedure for using VideoPoint is at the end of the experiment.
Start VideoPoint.
Click left mouse button while the pointer is anywhere inside the "about VideoPoint" dialogue box.
In the "open" dialogue box do the following.
Select the drive letter of the CD drive in which VideoPoint is located.
Select movies folder and the appropriate folder under movies (here the "PRU" folder).
Under filename select the appropriate file to be loaded.
Press "OK".
The "Number of points" dialogue box will appear. Make sure "1" is selected and press "OK". The movie and software should now be loaded.
On the menu bar select "Movie" and "Full Screen" using the left mouse button.
Record data -When the cursor is inside the movie screen it appears as a target. Place this target cursor on the rotating puck and press the left mouse button, the movie will advance one frame and the data is recorded. Repeat this process until all frames of the movie have been used.
Calibrate the movie.
Move the cursor to the "meter stick" tool button at the left of the screen (6th button from top) and click the left mouse button.
The "Scale Movie" dialogue box appears. Select continue with the left mouse button.
Put the target cursor on the top end of the meter stick in the first movie frame and press left mouse button - place the target cursor on the bottom of the meter stick and press the left mouse button.
Relocate the coordinate axis by placing the pointer on the axis and pressing and holding the left mouse button and dragging the axis to the center of the rotating wheel.
On the menu bar select "Movie" and "Normal Size".
Graph the data.
Select "Graph" tool button on tool bar at left side of the window with left mouse button. (8th button from top) - "Plot Series" dialogue box will appear.
The horizontal axes should be "time".
The vertical axis should be "Point S1" and "angle".
The angular velocity options should be highlighted by clicking the left mouse button when the cursor is on the word.
Press "OK" and the graph should appear and the data for the angular velocity should be added to the data table
Select "Graph" tool button on tool bar at left side of the window with left mouse button. (8th button from top) - "Plot Series" dialogue box will appear.
The horizontal axes should be "time".
The vertical axis should be "Point S1" and "radius".
The position options should be highlighted by clicking the left mouse button when the cursor is on the word.
Press "OK" and the graphs should appear and the data for the radius should be added to the data table
Transferring the data
With cursor inside table area click left mouse button to select table.
Put mouse in title area of table and click and hold left mouse button
and drag the
table to top of window.
Place the pointer on lower right corner of table (cursor should be double arrow) and drag the corner of the table to make the table larger so all the data can be seem.
Record the time and the angular position of data in data table. You will need to use the
scroll bar on the left side of the data table to see all of the data.
QUESTIONS:
1. Was energy approximately conserved in this process?
2. Was angular momentum approximately conserved in this process?
3. What is the mechanism that is the source of the change of rotational kinetic energy in this experiment?
4. Is the tension in the string to pull the puck into smaller path a constant force ?
5. What is the quantities that influence the moment of inertia of an object?
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