Rotational Inertia (Rotational Kinematics and Dynamics)

Transcription

1 PHYSICS LAB 8 SP211 Rotational Inertia (Rotational Kinematics and Dynamics) I. Introduction NOTE: Please take a stopwatch (or a wristwatch with a built in stopwatch) to lab if one is available to you; iphone works too.) The physics of rotational motion can seem mysterious. There are many unfamiliar concepts to be learned including angular velocity, angular acceleration, moment of inertia, and torque. In addition we need to know the relationships between angular and linear quantities. Consequently it is worth spending some time in the laboratory studying rotational motion. Toward that end we will determine the moment of inertia for a rigid configuration of masses. As usual we will compare the experimental results with theoretical predictions. II. Objectives At the end of this activity, you should: 1. Be able to calculate the Moment of Inertia of a relatively complex system, including the use of the Parallel Axis Theorem. 2. Be able to compare our predicted value of Moment of Inertia with that of observed and determine reasons disagreement. 3. Be able to observe the Torque due to Friction and see its effect on the system. Page 1 of 5

2 III. Needed Equipment Your instructor will show you the experimental setup, a sketch of the equipment that will be used in the first experiment of this lab is shown in the next diagram. Part of the equipment should look familiar since we used it previously in the Uniform Circular Motion lab. In this week's lab, a crossbar (threaded rod) and cylindrical masses will be attached to the shaft as shown. We study this system because we can do a fairly good job of predicting the moment of inertia. The general procedure will be to use a string to cause the system to rotate. (The string will exert a torque on the shaft.) The tension in the string will be controlled by a hanging mass and the torque will be calculated using the radius of the shaft and the tension in the string. We will separately evaluate the effect of friction by studying the system as it slows down due to friction. In all cases we will analyze the data using Newton's Second Law for Rotation, net = I. In other words, we will measure the rotational inertia of a rigid rotator by measuring its acceleration when we apply a known torque to it. IV. Turn in your Pre lab/homework problem if assigned. We will use the spreadsheet we built for homework to solve for our predicted Moment of Inertia value with our actual lab data. Page 2 of 5

3 V. Discussion Your instructor will demonstrate the experimental setup, the required procedures, and how to take data. Safety is job number one! VI. Procedure A. Preliminary Data: A.1. Measure and record the masses and dimensions of the components of your rigid rotator; use the homework problem as a guide. Don t forget, g = m/s 2. B. Prediction B.1. Use the measurements you made in Part A to predict the rotational inertia of your rotator. Substitute your measurements into the spreadsheet you built for the homework problem to make this calculation. Don t forget to include the uncertainties. (Mass of the shaft for those whose aren t removable is.4086kg.) Page 3 of 5

4 C. Experiment: Measure rotational Inertia as follows: C.1. Effective radius of the shaft: Because the string has some width, and the tension acts at the center of the string, the radius we must use to calculate the torque is larger than the radius of the shaft. To measure this effective radius, wrap the string around the shaft, as many complete turns as you have string. Count the turns. Then measure the length of the string required for that many turns. The effective circumference is length/turns; from that, calculate the effective radius; don't forget the uncertainty. C.2. Angular acceleration due to a falling weight: Use a wristwatch to measure the time required for the falling weight to turn the rotator through 15 to 20 complete revolutions more is better. Use the equations for uniformly accelerated rotational motion (UARM) to determine the angular acceleration. Do this three times and take the average and standard deviation. From that and the effective radius, calculate the tangential acceleration, which is also the translational acceleration of the falling weight. C.3. Tension in string and torque due to that tension: I claim that the tension in the string is not equal to mg. Draw a free body diagram for the falling weight, apply Newton s 2 nd law (NII), and solve NII for the tension. Use the measured value for the falling weight's acceleration from C2, just above. Then calculate the torque the tension exerts on the rotator. C.4. Correction for frictional torque: If not for friction, the angular acceleration would have been greater than we measured. (Dang ol friction!) To correct for that, measure the deceleration due to friction as follows: Remove the falling weight and give the shaft a spin by hand. Measure the time the rotator takes to slow to a stop while counting the rotations. Again use the equations for UARM to calculate the frictional angular acceleration. C.5. Put it all together to find the rotational inertia of the rigid rotator: The torque exerted on the rotator by the falling weight is (R effective )*(F Tension ). We don't know the frictional torque, but we have measured the angular acceleration it gave to the rotator. Add the magnitudes of the frictional angular acceleration from C4 and the angular acceleration from C2. Combine that with the torque from C3 to calculate the measured rotational inertia. Don't forget the uncertainties! Page 4 of 5

5 VII. Lab Report to Hand In: A. Spreadsheet you used to predict your rotator s rotational inertia from Part B; don t forget the uncertainties. B. Spreadsheet from Part C in which you calculate the measured value of your rotator s rotational inertia; don t forget uncertainties in each part! C. Discussion: Did your measurement agree with your prediction? A Yes or No answer will not suffice; explain your answer. VIII. Clean Up A. End of Lab Checkout: Before leaving the laboratory, please tidy up the equipment at the workstation and quit all running software. B. The lab station should be in better condition than when you arrived and more importantly, should be of an appearance that you would be PROUD to show to your legal guardians during a Parents Weekend. C. Have your instructor inspect your lab station and receive their permission to leave the Lab Room. D. You SHALL follow this procedure doing every lab for BOTH SP211 and SP212! Many thanks to Dr. Huddle for his assistance in producing this Laboratory procedure; specific references can be supplied on request. LCDR Timothy Shivok Page 5 of 5