Circular Motion Lab PDF

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Circular Motion Lab...

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3/19/2021 PHY 133 TA: Sergey Alekseev Circular Motion Lab

Introduction Circular motion is the movement of an object which rotates around a specific point while also moving through space. Position, speed, and acceleration can all be used to describe circular motion. Therefore, all the points on a uniformly spinning object will spin at the same rate and have the same angular distance, but the speeds of these objects will vary. This is because the speed depends on how far away a point is from the center of rotation. We are able to describe this using the equation v=rw and we can hypothesize that the further away the point is to the center of rotation, the larger the velocity. Also, an object that moves in circular motion is always changing its direction and therefore even though the magnitude of the object remains unchanged, the acceleration is constantly changing. This is called centripetal acceleration, which moves perpendicular to velocity. This acceleration is defined as (ac) and its relationship to velocity can be shown with the equation ac= (v^2)/ r with r being the radius and v being velocity. In this lab we will use the accelerometer and gyroscope to measure angular velocity, linear acceleration as we rotate the IO Lab around the z-axis. After this we determine the distance between the center of the IOLab and the accelerometer. The distance should be consistent.

Procedure 1. Measure the distance between the IOLab center of mass and the accelerometer. 2. Throw the device in the air so it rotates around the z-axis and record this motion. 3. Using components find the total centripetal acceleration 4. Find the angular speed of the IOLab as it is in the air 5. Repeat steps 2-4 twice.

6. Make sure to throw the device with different angular speeds as you repeat these steps 7. Make a plot of (Ac vs w) and a plot of (Ac vs w^2) 8. Find the radius for comparison

Results The distance between the center of mass and the accelerometer is .04m or 4 cm. We will use this to act as our radius. Figure 1 - Run 1 Angular speed and acceleration

Figure 2 - Run 2 Angular speed and acceleration

Figure 3 - Run 3 Angular speed and acceleration

Figure 4: The measured values of ω versus ac. The graph has a power trend line. Table 1

Figure 5- ω2 versus ac, measured by the iOlab device. There is a linear trend line.

Table 2

(w)^2

ac

156.8

6.272

245.73

9.8292

338.08

13.5232

Radius in figure 4 is 0.399m and the value of the radius in figure 5 is .04m. The measured distance from the gyroscope to the accelerometer is 0.04m.

Calculations Run 1: Ax = 2.279 m/s2 ± 0.70 m/s2 Ay = -7.225 m/s2 ± 0.38 m/s2 (Ac1) = =√(2.279)^2 +(7.225)^2 = 7.579m/s2 ∆S = √∆ A2 +∆ B2=√(0.70)^2 +(0.38)^2= 0.796 Run 2: Ax = 4.014 m/s2 ± 1.3 m/s2 Ay = -9.732 m/s2 ± 1.2m/s2 (Ac1) = =√(4.014)^2 +(9.732)^2 = 10.527m/s2 ∆S = √∆ A2 +∆ B2=√(1.3)^2 +(1.2)^2= 1.769

Run 3: Ax = 6.353 m/s2 ± 3.7 m/s2 Ay = -21.079 m/s2 ± 2.4m/s2 (Ac1) = =√(6.353)^2 +(21.079)^2 = 22.0155m/s2 ∆S = √∆ A2 +∆ B2=√(3.7)^2 +(2.4)^2= 4.41

Uncertainty (ac)/(w^2)= r (6.272)/(156.8)=.04 (9.8292)/(245.73)=.04 (13.5232)/(338.08)= .04 All these values are identical to our measure radius % error is yielded over expected so .04/.04 = 100% accuracy, 0% error

Discussion From the data that we were able to collect and calculate we are able to see the different trends. One of these is that during the throw the acceleration is positive in the x axis but negative in the y axis. This holds true for all three throws. In the experiment, we were able to measure the centripetal force by using the acceleration in the x and y directions. Using this we were able to find the acceleration of the IOLab device. The gyroscope tells us the angular speed of the device. We can plot centripetal acceleration vs. angular speed to find the radius of the rotation. Figure 4 and figure 5 shows us this relationship. These two radiuses are 0.0399 and .04, which compared to our measured radius of 0.04 are basically equal with a 100% accuracy. Therefore we can justify our hypothesis that the further away the point is to the center of rotation, the larger the velocity. In Figure 4, we expect to see a parabolic plot, which we do. In Figure 5, we expect to see a linear plot. In figure 4, we used a power trendline, which gave a curve with the equation: y=0.0399x^2.0018 . In figure 5, we used a linear trendline with the equation: y=0.04x -2E^-14 . In both equations, the coefficient should be compared to the measured value of the radius. The coefficients are as previously stated nearly identical to our measured value of 0.04 so a relationship between tangential velocity and radius can be proven. Although our measured and calculated values line up with one another, there could have been inaccuracy from human error when tossing the IOLab device in the air. The error of the measured value of the radius is small so that is unlikely to have affected the results significantly. This lab allowed us to perform three experimentations but we can conclude that if we keep repeating trials then the results should be clearer and closer to the measured value of .04....