Circular Motion Lab-2

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Stony Brook University *

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121

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Physics

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Dec 6, 2023

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Circular Motion Lab Introduction: Analogous to linear kinetics, circular motion can be expressed through studying the acceleration, position, and speed. The difference between the two is that the representation of the distance traveled, which for circular motion is described as an angle, θ, which is measured in radians and angular speed and acceleration is measured in rad and rad^2. All points of a spinning object have the same angular velocity, meaning that all of the points are spinning at an equal rate and eradicating the same angular distance. Depending on how far the point of interest is from the fulcrum will determine the tangential speed of the points. The fulcrum in this lab is located at the center of the iOLab device and can be represented as the G in the red square on the front of the device. The direction of motion constantly changes, yet, the size of the tangential velocity of all the points are the same. Owing to the change in velocity, the object has the centripetal acceleration (a c ); directed toward the center of the circle. To determine the centripetal acceleration, we use the following equation; a c = 𝑟𝑤 ^2 . In this equation, r is the radius of the circular motion and v is the tangential velocity. During this lab, the device will be tossed up into the air, resulting in it rotating about its z-axis. In the midst of the motion, the accelerometer, represented by A, will measure the acceleration as it eradicates a circle around G. With the completion of this lab, we will be able to determine the distance between points A and G and compare it to the measured value. Procedure: 1. Plug dongle into the computer and make sure the iOLab device is turned on 2. On the front of the iOLab device, using the tape measure, measure the distance between the center of the mass, marked with G and the accelerometer, marked with A 3. Begin recording 4. Toss the device in the air so that it rotates about the z-axis 5. Using vector addition of the x and y componenets of acceleration, determine the total acceleration of the centripetal 6. Determine the angular speed of the device as it is in the air 7. Repeat the previous steps as you throw the device at different angular speeds *by slightly increase or decreasing the force with which the device was thrown 8. Plot vs. acceleration 9. Plot vs. acceleration 10. Determine the radius of the rotation and compare it to the measured value from step 2 Results:

Figure 1. Data from the first throw Figure 2. Zoomed in data of the first throw at a slow paste

Figure 3. Data from the second throw Figure 4. Zoomed in data of the second throw at a medium paste Figure 5. Data from the third throw

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Figure 6. Zoomed in data of the third throw at a fast paste rad/s a c (m/s^2) Throw 1 *slow -19.312 4.844 Throw 2 *medium -23.473 7.328 Throw 3 *fast -24.135 7.290 Figure 7. Plot of acceleration

Figure 8. Plot of acceleration Calculation: Error Analysis - [0.0375 - 0.04/ 0.04] *100 = 6.25% - [0.0315 - 0.04/0.04] * 100 = 21.25% * The percent error values are relatively low Discussion/ Conclusion: Using the slope of the two equations, the radius resulted to be 0.0315 radians and 0.0375 radians. These values in comparison to the measured value of 0.04 m from the start of this lab exemplify that this lab was a success. We were able to determine the radius of the rotation of point A on the iOLab device due to the numbers being close and the percent error being low. The values for ax are always positive, which explains why the x on the device is moving in a positive direction in the midst of the device being in motion. On the other hand, the values of ay are always negative, which is why the y on the device is moving in a negative direction while the device is in motion as to where the two points are. While completing this lab, human error could have occurred and altered the data. For example don't throw the device to different pastes to receive different data. If this issue occurred, one’s data would have been less accurate.

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