I am very confused! Please answer 5 - 15 of the analysis portion. I am so lost.

Link to video: https://physics.highpoint.edu/~atitus/videos/

Scroll down to 'Videos' and find the one titled 'Uniform circular motion of a bicycle wheel' and click on 'bicycle-wheel.mov'

Link to the tracker install: https://physlets.org/tracker/

Please read through the instructions, all of the relevant figures and graphs are labeled as "figure 5.2" for example.

Lab 5: Video Analysis of a Bicycle Wheel in Uniform Circular Motion Goal In this experiment, you will measure and graph the x-position, y-position, and angle as a function of time for a sticker on a bicycle wheel rotating in a circle at constant speed. You will use the data to determine the sticker's linear speed, angular speed, period, and radius. Introduction Suppose an object moves counterclockwise along a circular path. Figure 5.1 shows an object at intervals of 1/30 s between the rst image A and the last image G. l) G A Figure 5.1: An object moves in a circular path. The xposition of the object for each image is shown in Figure 5.2. o L c l- B F L' D C B Figure 5.2: The xposition of an object moving in a circular path. The radius of the circle is R. We can calculate the object's x and )1 position at any instant. Let's look at the object when it is at position C. The triangle showing the object, its x-position, and its yposition is shown below. Using this angle, the xposition and yposition can be calculated as x : R cos(9) y = R sin(6) For an object moving in circular motion with a constant speed, the angle 8 that the object makes with the +x axis changes at a constant rate. The rate that the angle changes is called the angular speed. To calculate angular speed, you measure how much it turns (A9) and divide by the time interval. Thus, 9g At CU: Figure 5.3: The x and y components of the object's position. If B is the angle at any instant t and if 60 is the initial angle at t=0, then 9% t w: 6 = wt+90 Thus, the x-position and y-position of the object at the clock reading t is Roos(wt + 60) Rsin(wt + 90) IE 39' As a result, the x-motion and y-motion each resemble simple harmonic motion. The linear speed of the object is distance traveled per second. It's easiest to consider one complete rotation. The distance traveled around a circle is the circumference. The time for one revolution is the period. Thus, the linear speed of the object is 27rR T ll = The angular speed during one revolution is (o = 27t/T. Therefore, we can write the linear speed as v = wR where a) is in units of radfs. It is typical to drop the magnitude symbol and vector symbol and write the speed lev| more simply as v. Procedure 1) Download the video bicycle-wheel.mov. This video was recorded at 300 fps, though it plays back at 30 fps and appears in slow motion. 2) Open Tracker and import the video. 3) Open the Clip Settings window by clicking on the Clip Settings icon (shown in Figure 4) which is part of the video control toolbar that is below the video clip. E Figure 5.4: The Clip Settings icon. 4) In the Clip Settings pop-up window, enter a frame rate of 300 fps, as shown in Figure 5.5 Clip Settings [E Start frame;30 _ Step sizezi' 17 . End frame:4.5711 . Start timeiDOO 5 Frame rate:.'300 Is Frame dtzi .33E3 s! l OK I Cancel l Figure 5.5: The Clip Settings icon. 5) Go to the rst me of the video and use the meterstick to calibrate distance in the video. vi Use this icon ., . and calibrate the diameter of the wheel to 60cm. 6) Advance to the next frame (frame number 001). 7) Place the origin at the axle (at the center of the white disk at the hub of the wheel in the video). 8) Since there are 300 frames of video recorded per second, the time interval between frames is quite small. As a result, we can skip frames between marking the ball and thus take fewer data points. Click on the Step Size button, as shown in Figure 5.6 and change it to 5. -.L_ 000 100 J.\" .- 9 AV 411' 1.: A . _ Step Size I :_. ,WIFE"!'EPJ,'99',|'3,'!:,5!9!'-@9 Figure 5.6: Change the step size in order to skip frames. 9) Click the Track button in the toolbar, click on new and select a new point mass. 10) Make sure the video is on the rst frame. 11) Hold the shift key down and click once on the green sticker that is on the bicycle tire. The video will then advance 5 frames. Continue to mark the green sticker for a total of 4 revolutions. If you are only displaying the last few marks, then it will look something like Figure 5.7. Figure 5.7: Marks for the green sticker on the rotating bicycle wheel. Analysis 1) Right-click on the x vs. t graph and select Analyze. 2) Check the Curve tter and click on sine. 3) [n the curve fit pane, Click the Fit name and change into sine. Then, click the button Clone , and select \"Sine.\" Click Add to add a parameter d with value 0. Edit the Sinusoidl function to be a >t= cos(b * t + c) + d, as shown in 5.8. The additive constant d will shift the curve t up and down by a constant as needed, though it should be 0. 4) The Autofit algorithm does not do well with sinusoidal curves. Thus, you will need to adjust each parameter manually. When you get these values fairly close, then you can do an Autot. It helps to start with some reasonable values. So make some approximate guesses for the following functions based on the curve: FitBuilder ' 33 _ ii . 2" '2: 1 :: E Fit Namezl Sinusoidl jvi New ' Clone Delete! Parameters F'JNI'I' EXP [Q 599'? Expression a'cos(b*x+c)+d Figure 5.8: The Fit Builder is used to fit a curve to a user-dened function. d shifts the curve up or down. It should be zero [or close to zero]. a is the maximum value on the curve. What is approximately the maximum value of a? Enter this into the box for a. b is the angular velocity, 21t/ T. What is the approximate period of the oscillation? Use it to calculate an approximate value of b and enter this value into the box. c is the phase. Once you set a and b, it will be easy to determine c. It shifts the curve right or left. You can adjust this manually without knowing the initial value. If you begin with approximate values, you can click in the Parameter Values box and click the up and down arrows to make small adjustments. You can also change the step size as you hone in on the best value for the parameter. Adjust each parameter by very small amounts (steps of 0.1%) until you get the best curvefit possible. An example curve-fit is shown in Figure 5.9. 5) What are the curve parameters and the fit equation for the best-fit curve? 6) From the curve fit, determine the radius of the sticker R. 0.3 0. 2 0. 1 x -0.0 -0. 1 -0.2 -0.3 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Fit Name: Sinusoid1 Fit Builder.. Parameter Value a 3.000E-1 Fit Equation: x = a*cos(b*t+c)+d 2.275E1 : 0.1% -1.1256-1 Autofit rms dev: 6.314E-3 0.000EO Figure 5.9: The best-fit curve for a point on the wheel. 7) How does your result compare to the measured radius of the sticker which is 30 cm? 8) From the curve fit, determine the angular velocity of the wheel w. 9) From the curve fit, determine the initial angle of the green sticker 00. 10) What is the period T of the wheel? 11) What is the linear speed v of the green sticker? 12) Close the Data Tool window and return to the main Tracker window. Change the graph to plot y vs. t. Right-click the graph and select Analyze . Repeat the same procedure as before, out this time fit a curve to y = a * sin(b * t + c) +d. 13) Record the values for the curve fit and compare to what you found when analyzing x(t).14) Close the Data Tool window and return to the main Tracker window. Change the graph to plot 0 (the rotation angle) as a function of t. Right-click the graph and select Analyze . Your graph of 0 vs. t will look like Figure 5.10. Data Tool File Edit Display Help sticker Plot Fit Statistics Coordinates Slope Area Data Builder... Refresh Help markers IV 25 lines IV style 20 axis horiz vert row 0 o 0.017 0.259 15 0.033 0.644 0.05 1.012 W NI 0.067 1.383 10 0.083 1.761 0.1 2.146 6 0.117 2.557 0.133 2.919 8 0.15 3.316 0.167 3.694 10 0.183 4.076 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 11 0.2 4.462 12 0.217 4.841 13 0.233 5.239 Fit Name: Line Fit Build Parameter Value 14 0.25 5.63 22.733 15 0.267 5.998 Fit Equation: 0 = a*t + b -0.084 16 0.283 6.387 17 0.3 6.752 Autofit rms dev: 2.659E-2 Look 0.317 7.11 Drag table columns to yellow (horizontal axis) or green (vertical axis) for curve fitting non-editable Figure 5.10: 0 vs. t. 15) Do a linear curve fit as shown in Figure 5.10. From this curve fit, record the angular velocity w. Further Investigation (extra credit) If the wheel is instead rotating clockwise, how would it affect the graph of 0 vs. t? How would a be different