Lab Activity Phy223 Rotational Mechanics, Part II: Swinging Stick Lab Activity Phy223 Rotational Mechanics, Part II: Swinging Stick Names: Analysis: 1. Create a graph showing the period T as a function of x, the distance between the axis of rotation and the center of mass. 2. Use your graph to find your experimental result for * (the distance with a minimum T) and the corresponding period I'min . Swinging Stick C. Finding the theoretical values for Knin and Imin The swinging stick is an example for a physical pendulum. The physical pendulum is covered in Introduction section 15.6 of your textbook. You can also check the video posted online ("Pendulum oscillations" in the Week4 module). In this activity you will find the minimum period of a swinging stick (a roughly 8-foot-long piece 1. Draw an extended FBD for the swinging stick at a point half-way through an oscillation of 1x2 nominal lumber) both theoretically and experimentally and compare the results. (maximum amplitude). Important hint: you can draw the FBD with the stick at the left-of- equilibrium position shown in the figure above or in the right-of-equilibrium position as shown in figure 15.20 of your textbook. Note that the angle e is measured counterclockwise from the Procedure and Instructions for Report equilibrium position. This means that e is negative in the figure above or positive in figure 15.20. 2. Use the parallel axis theorem to create an equation for the moment of inertia for your stick A. Abstract as a function of x(the distance the axis of rotation is away from the center of mass) Give a brief description of what you did. What is the purpose of this lab? 3. Write out the equation for _ =Io about the axis of rotation (not the center of mass) using information from #1 and #2 above. What force is exerting the torque to speed up and slow down the stick? Is / the moment of inertia about the center of mass or not? B. Finding the experimental values for Xwin and Twin 4. Solve the differential equation you obtained in step 3. Use section 15.6 in your textbook for Your goal is to find the period 7 of oscillation as a function of x, the distance between the axis of guidance. You will get an equation for the angular frequency @ as a function of x. rotation (pin) and the center of mass (cm). You will then use your data to experimentally find the distance Xi, for which the period Thas its minimum value Im.. 5. Rewrite this equation to determine a function for the period 7(i.e. express @ in terms of 7 and solve for 7). Experimental Setup: 6. Use calculus to predict the position x; for the minimum period and the value for the 7pin minimum period . . In Excel, create a graph of T vs. x, and include it in your report. axis of rotation D. Conclusions center of mass 1. Compare - using a graph overlay - your theoretical function for the period to your experimental function. cm angle 0 should not exceed 10 2. Compare your theoretical and empirical values for * and Tm. Determine the percent difference * min sherry - X min, experim Discuss your results. * minthey 3. Give possible sources of error and discuss their significance. Procedure and Data: 4. Discuss the physical meaning of the minimum of the period. That is, what is happening physically that reduces the period and then increases it again? Hint: in your equation for T vs. X, 1. Use every hole, starting with the first hole from the center of mass, as the axis of rotation. what is the physical meaning of the numerator and denominator? 2. For each hole: take two or three trials to measure the period 7. Make sure to keep the amplitude low (less than 10). Keep friction to a minimum. Record all data in an Exce spreadsheet (i.e. all values for 7, their average, and the distance x) and include it in your report