Lab 3 - CENTRE OF MASS AND MOMENTS OF INERTIA INSTRUCTIONS This laboratory expects that you have viewed the Week 7 in detail in module in Canvas and completed the PreLab Test 3 available in Assignments in Canvas. In this lab you are tasked to identify i) the centre of gravity of an unusually shaped object (D), ii) the mass of an unknown object (M2), iii) the mass of the balance arm used (M3) and iv) to identify the moment of inertia pre-factors for rotation of the balance arm about its end and about its centre. You cannot use the electronic scales for these tasks but must "think up" methods that utilize the concepts of torque, centre of mass and moments of inertia. The laboratory supervisors will collect your and the class's data from which you must calculate the mean and standard deviation of D, M2, M3. Report: You must create a report and it should contain the filled in worksheet. Submit the report online in Canvas within 7 days of this laboratory. Required Formula: mean standard deviation Centre of mass Moment of Inertia N (X) = = > i=1 Xi , 0 = ??(X; - (?))2 Xcm - N-1 I = Emir2 > |+2dm i Apparatus provided: A plastic shape containing 3 randomly placed holes; a 1 m ruler as a balance arm containing holes at 50 cm and 70 cm; a smooth round nail with some cotton and scissors; 2 x 50 g masses, a 50 g hanger and an unknown mass M1; retort stand, boss head and clamp. Experiment 1: Determine the distance D from the centre of gravity (Xcm, ycm) to the point X Clamp the nail horizontally to provide a fixed pivot point above the table. Locate the plastic object on the pivot point such that when you let go the object swings. Discuss with your lab partners why does the object swing. Can you describe the torque (its magnitude and direction) as the object swings? Does the object's weight force change during the swinging? After a while the object stops swinging. Why is there no rotational acceleration at this time? You should now be able to identify a line upon which the centre of gravity must lay. Use the other holes to pin point the centre of gravity. Measure to 2 significant figures the distance D to the X, enter this value in the excel spread sheet provided by the lab supervisor. Fill out your table in Experiment 1 using data collected by your row. Experiment 2: Determine the unknown mass (M2) You have been told that you can't use the electronic scales for this task but no-one said you could not build a set of scales yourself! After consulting with your lab partner and reminiscing about your childhood adventures on see-saws, build your apparatus. Once you have observed static equilibrium you should be able to sketch a free body diagram and fill out your worksheet. Provide your measured value of M1 to the