Kevin Nguyen
Lab Partners: Jose Rodriguez, Kevin Tran
Date performed: 03 April 2017
Purpose of this lab: The purpose of this lab wass to teach us that if the motor spins at a faster angular speed, the radius between the mass and the central shaft along with the angle will increase. Using that fact, we must establish a relationship between angular speed and angle.
Theory/ Introduction: We established the relationship between the angular speed and the angle below.
From the triangle on the upper right side, we were able to find the angle by finding the length of the string and the height of the apparatus minus the height of the mass above the ground.
We identified the forces going in the horizontal (x) direction and vertical (y) direction. Since the ball's centripetal acceleration was geared towards the central shaft, it was safe to say that the sine of tension force is equal to the centripetal force. Since gravitational force and tension force were the only forces acting on the masses in the vertical direction, the relationship of cosine of tension and gravitational force can be established. The forces in x and y direction was divided and the angular velocity was solved for, establishing the relationship between the angle and the angular velocity. After recording data for the five trials, we compared the calculated angular velocity to the recorded angular velocity to see if the relationship is accurate. We had done this by graphing the recorded angular velocity on the y-axis and the calculated angular velocity on the x-axis, made a linear fit model, and analyzed the slope of the line. The slope of the line told us how closely related the two data points are. The closer the slope of the line is to 1, the stronger the relationship is between the recorded angular velocity and the calculated angular velocity. If the correlation given from Logger Pro linear fit is also close to 1, it also implied a strong relationship between the calculated angular velocity and the recorded angular velocity. A strong relationship between the recorded angular velocity and the calculated angular velocity supported the relationship that we established between the angle and the angular velocity.
Summary
In the lab, we collected data from this apparatus to support our relationship that we have established above. We were told to observe the apparatus below.
In the picture, the motor was on top of the tripod. A mass hung at the end of the string. We measured the height of the rod that holds the string from the ground, the height above the ground the mass is at when it is spinning, and the length of the string the mass is attached to. In order to get several data points, we recorded the height the mass was above the ground at different angular velocities. After we finished taking data, we calculated the angular velocity using the data of the heights of the mass above the ground and the apparatus, the distance between the mass and the central shaft, and the length of the string attached to the mass. After calculating the angular velocity, we graphed our recorded angular velocity on the y-axis and the calculated angular velocity on the x-axis, made a linear fit for the data plots, and analyzed the slope of the line.
Measured Data:
Calculated data:
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| Calculated angular velocity is in the bottom right. The calculated angle is on the bottom left. |
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| Calculated angular velocity (x) vs Recorded Angular velocity (y) |
The graph above showed that the slope was 1.053 and that the correlation between the calculated and recorded angular velocity was 0.9981, or 99.81% correlation. With a slope value and correlation value very close to 1, those values imply that the relationship between calculated and recorded angular velocity is very strong. A strong relationship between the two also imply that the relationship we established between the angle and the angular velocity is valid.
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