PURPOSE: To study and analyze the motion of an object undergoing constant angular acceleration.

THEORY: An object undergoing constant angular acceleration should obey the following equations.

1.  2. 

3.  4. 

5.  6. 

where D q is the change in position (angular distance traveled), t (or D t) is the elapsed time, w _o is the initial angular velocity, w _f is the final angular velocity,  is the average velocity, and a is the angular acceleration.

EQUIPMENT: Computer, VideoPoint Software, graph paper and straight edge.

PROCEDURE: There are several video files from which to chose. From the "DSON" subdirectory chose the one named dosn014. With the VideoPoint software mark the position of the object as it accelerates. There is a step-by step procedure at the end of the laboratory for using VideoPoint for this experiment. You should have reviewed the introduction provided with the VideoPoint CD and the Walkthrough on the CD or the Web sight. This data can be copied into the provided data table. Record the angular position q and time t on the provided table and calculate the angular velocity and angular acceleration for each interval possible. Use this data for the following graphs.

Graph the results. Make two graphs q verses t, and w verses t. Use the graphs and information in the data table to find the following. Make only one graph per page and make the graph take up at least half of the page both horizontally and vertically. Make sure you label the graph, the axis, and indicate the units the numbers on the graph represent.

1. The slope of the angular velocity verses time graph. Draw the best straight line through the data (do not play connect the dots). The slope of the line is the rise over the run for the line drawn through the data. Remember that the numbers on the axis have units and so will the slope.

2. Find the average angular acceleration for the car for the entire experiment. Add up all of the accelerations and divide by the number of accelerations added.

3. The slope of the angular velocity verses time line should be the average angular acceleration. Find the percent error in agreement of the angular acceleration calculated from the slope of this line and the average of the angular accelerations from the table. Treat the average angular acceleration as the expected average

QUESTIONS:

1. Are the equations for angular motion and linear motion the same except using different symbols?

2. What is a negative angular acceleration?

3. Consider the angular velocity Vs time graph. If the scale used for plotting the velocity were changed the angle at which the line through the data is drawn would change. Would this change the slope of the line?

4. On the first frame of the movie the diameter of the wheel was gives. Use this diameter and calculate the last angular speed of a point on the rim of the wheel from its angular speed.

5. If the angular acceleration had been zero what would the graph of angular position as a function of time have appeared?

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 "dson" 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 a white dot on the rotating wheel 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. Change the "known length" to 0.10 and 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 at the 10 cm mark of the meter stick and press the left mouse button. Place the target cursor at the 10 cm mark 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 position, velocity, and acceleration options should be highlighted by clicking the left mouse button when the cursor is on the word.

Press "OK" and the graphs should appear.

Fit equations to the graphs.

With cursor on each graph click left mouse button then select the "F" flag and click left mouse button again.

By using the left mouse button select the following.

For angular position choose" type of fit" = "polynomial" and "order of fit" = "2" and "OK".

For the angular velocity select "type of fit" = "linear" and "OK".

For the angular acceleration select "type of fit" = "Average" and "OK".

For each graph the equation or average is displayed with the plots.

For position Ax² + Bx + C (A = 1/2 a ; B = w _o ; C = q _o ; and x represents to t).

For velocity Ax + B (A = a ; B = w _o ; and x corresponds to t).

For acceleration the average is the average acceleration.

These values should be compared to the corresponding values from your plots

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.

Average acceleration = ________

Acceleration from slope = ________

% error in acceleration = ________