Question

MOMENT OF INERTIA LAB Apparatus Only (P3) With Masses (P4) With Block (P5) Setup You have a T-shaped apparatus that can spin about a vertical axis. One end of a light string is wrapped around the vertical shaft of the apparatus. The other end passes over a pulley and has a known mass hung from it to establish tension in the string. By measuring the acceleration of the hanging mass, the rotational inertia of the apparatus can be determined. Specifically, the tension in the rope causes toque on the apparatus, and the linear acceleration of the mass is related to the angular acceleration of the rotating piece. la = 1 = (F-fr (missing step is the assigned question] I = (mg - mapa It is important to be clear that m is the hanging mass and r is the radius of the shaft of the rotating apparatus. Do not confuse them with the mass and distance terms for additional weights added later in the procedure. There is some frictional force fresisting motion of the system. Procedure P1) You measure the diameter of the apparatus' rotating shaft to be 1.23 cm. P2) First, you attempt to determine the frictional force. With 6.0 grams hanging from the string. the mass will descend at a constant speed after being started in motion P3) The 6 grams is removed, and a total of 85 grams is hung from the string. With only the bare apparatus, shown in the left-hand picture at the top, you measure the acceleration of the hanging mass as it descends. The data for three trials are given in the table below. P4) Two 200 gram masses are attached to the apparatus, one on either side. This is illustrated in the center picture at the top. The center of each mass is 14 cm from the axis of rotation. Once again, you measure the acceleration as the 85-gram hanging mass descends. PS) You remove the masses and attach a rectangular steel block to the top of the apparatus. This is illustrated in the right-hand picture at the top. The block's mass is 1926 grams, and its other dimensions are shown below. The center of the block lies on the axis of rotation. Once again, you measure the acceleration as the 85-gram hanging mass descends. 12.75 cm 2.80 cm 7.60 cm Data Trial 1 2 3 Apparatus Acceleration (m/s) 0 .0176 0 .0196 0 .0189 Apparatus+Masses Apparatus+Block Acceleration (m/s) Acceleration m/s) 0.00314 0.00559 0.00307 0.00560 0.00303 0.00567 Analysis A1) Using the data from P2 and P3, determine the rotational inertia of the apparatus. A2) Using the data from P2 and P4, determine the rotational inertia of the system from step P4 A3) Using the data from P2 and P5, determine the rotational inertia of the system from step PS. A4) Combine the results of A1 and A2 to determine the rotational inertia of only the two added masses. Compare this to the theoretical value for point masses in the same configuration and give a percent error. AS) Combine the results of Al and A3 to determine the rotational inertia of only the block. Compare this to the theoretical value for a rectangular block spun about its center and give a percent error. Question Q1) By applying Newton's 2 Law to the hanging mass, give the missing steps in the derivation of the inertia equation at the top of the first page. Could you answer the analysis questions and the question at the end.

Answer 1