Video Analysis of Circular Motion
In the first part of this activity, you will analyze the changes in the positions of blocks on a turntable as they move with constant linear and rotational speeds around a circular path. Position-time, velocity-time, and acceleration-time graphs of both linear and rotational motion will aid your understanding of this type of periodic motion.
Linear Motion Analysis:
6. After the video has been marked, go to the coordinate systems box and double-click on Pt.
on the Point S1 line. Change the units to m and deg and click OK. Do the same for Point S2.
Change the masses of the two blocks to the value given in the first few frames of the video.
7. Make graphs of position-time, velocity-time, and acceleration-time for both x and y
components for Point S1. Use the add button on the graphing menu to place these in the
same window.
8. Paste these three graphs in the appropriate box on the next page after making any needed
corrections to position marks in the video and changing the vertical scale in the graphs as
needed.
9. Now make graphs of position-time, velocity-time, and acceleration-time for both x and y
components for Point S2. Use the add button on the graphing menu to place these in the
same window.
10. Paste these three graphs in the appropriate box on the next page after making any needed
corrections to position marks in the video and changing the vertical scale in the graphs as
needed.
Questions:
A. What mathematical relationship do the shapes of these graphs represent?
B. Compare and contrast the graphs of Point S1 with those of Point S2.
C. Is the motion periodic? If so, what is the period (time for one cycle or revolution) and
frequency (number of cycles or revolutions per second)?
D. When the horizontal speeds are at a maximum, the vertical speeds
are at . Where are the objects located at these
times? Show on the diagram of the turntable.
D. When the vertical speeds are at a maximum, the horizontal speeds
are at . Where are the objects located at these
times? Show on the diagram of the turntable.
E. How many times do the horizontal and vertical position-time
graph curves intersect? Show the positions on the turntable
where the objects are located when these curves intersect.
F. How many times do the horizontal and vertical velocity-time
graph curves intersect? Show the positions on the turntable
where the objects are located when these curves intersect.
G. How many times do the horizontal and vertical acceleration-time
graph curves intersect? Show the positions on the turntable
where the objects are located when these curves intersect.
11. Now make graphs of position-time, velocity-time, acceleration-time, and force-time for the
magnitude of Point S1. Place these in the same graph window.
12. Even though these curves appear sinusoidal, there is actually a linear relationship
among these variables. The problem is that the horizontal and vertical scalings of the
movie are not the same.
13. Rescale the y-axes of these graphs to obtain a better pictorial representation and add a linear
fit (or average value if graph is horizontal) to each of these three graphs.
14. Paste the graphs in the following box.
15. Do the same for Point S2 and paste these graphs and equations in the following box.
Questions:
H. Compare these graphs of Point S1 and Point S2.
I. Each of these curves approximates a horizontal line. Usually this means that the variable is
constant. How can the magnitudes of the position, velocity, and acceleration of the blocks
on the turntable be constant, when the horizontal and vertical components of each were not?
J. What is the constant value of each graph?
What information does each of these constants tell us about the motion?
K. How should the radius of the circular path, the period of the motion, and the speed of the block
on the turntable be related?
Angular Motion Analysis:
16. Now make position-time, velocity-time, and acceleration-time angular motion graphs. To
graph these, you must choose angle (theta) for Point S1 and then for Point S2 in the graphing
choice menu.
17. Change the scales of these graphs as needed to produce a better display of these curves.
18. Add a linear fit equation (or average value if graph is horizontal) to each of these three graphs.
19. Paste these graphs in the following boxes.
Questions:
L. Compare/contrast the angular motion graphs of the two marked objects.
M. What units are used to describe the angular position?
N. What units are used to describe the angular velocity?
O. What units are used to describe the angular acceleration?
P. How would you convert these to units of revolutions?
Q. What are the shapes of the angular position graphs?
What does this shape represent?
R. Describe if/how the angular velocity and acceleration graphs support the meanings of the
angular position graphs.
S. How are the magnitudes of linear velocity and angular velocity related (if you were given one,
how could you calculate the other one)?
Extension: (not required, but should be given thought)
These objects moved clockwise in their circular path around the center of the turntable. Compare and contrast the linear and angular motion graphs that would result if the objects were rotating counterclockwise instead.
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