oday we will check our moment of inertia theory predicions Dy Overview: The mome
ID: 2304082 • Letter: O
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oday we will check our moment of inertia theory predicions Dy Overview: The moment of inerti motion. Our basic equation, with an object that a l of an object gheasures how difficult it is to change the object's rotational it to rotate, is t la. For the has one torque applied to cause experimental part of our lab today, we will apply & torque r to a calculate the moment of inertia I value disk, measure angular acceleration ? . and s a theoretical value for its moment of inertia I MR. We will calculate mass and radius values and compare to the e xpgrimental value. Procedure: CoeTy2R Measure the mass of your aluminum disk on the electronic ruler first and record below. Also measure the radius of the disk using your caliper Measure the diameter of the disk with a by inserting a caliper jaw center opening of the disk and holding the other jaw at the edge. Record that also below. Divide your values to get an official radius value. To your uncertainty, use either half of the difference between the two radius measurements or 0.05 cm, ver is larger. Convert both the mass M and the radius R into standard (MKS) meter and kilogram units. Disk mass M- 2. m u123 ka no uncertainty needed Diameter13.5 cm half this radius (cm Radius R with calipers Average-official" radius R value:a,74 ± 05cm cm -aoutu±??XS meters,? There is a smaler metal hub that we will attach on top of the aluminum disk on the air table. diameter of this hub with the caliper, and have your partner measure this diameter also. the radius of this hub. Average the two radius values and use 0.005 cm as the uncertainty, whichever is larger. Convert this to meters also. Measure the by two to get either half the difference between the values, or Divide Hub radius r your measuremetm partner measurement- Average r valuesa?94 cm± 05 cm -e0284 meters ±?0005 meters,2% ght puley Now set up the air table with the large disk and attached pulley as directed by your instructor and the model unit. Mount a pulley on the 8ssedge of the lab table. Turn on the air supply slowly so that you can see the disk can spin without dragging and notice roughly how much air that m takes. You want to be confident friction is not significant, but don't blow so hard that you blow out the hoses. Then turn off the air and connect the lightweight string (not heavy string here) to the hub. You can use a small piece of tape if needed. Run the string from the disk over the pulley on the table to a hanging 5 gram mass as shown in the diagram. You will want the hanging mass to fall 50 centimeters from a starting point till it hits the ground. You should be able to tape a meter stick in position to get the 50 centimeter distance set up. Once set, you might put a small ink mark on the string perhaps at the end of the disk so you know at what location you should release the system. ight Version: F17 Page 1/4 ma Colulotetl épe ctedExplanation / Answer
1) The tension would cause a 1% change in the value taken for torque, in which we had a 2.14% error in radius measurements and nearly 6% in angular acceleration. Therefore the 1% would not change the final theoretical answer significantly and would fall in the same range.
(I see you have already draw the free body diagram on the right hand side top corner on page 3)
2. a) If the Hub were to be considered, the moment of inertia of the hub (using parallel axis theorm) would be added to that of the theoretical value already calculated.
b) This would increase the theoretical value and cause the difference between experimental and theoretical values to increase.
3) If friction was considerable, the time taken for the mass to reach down would be larger, thereby decreasing the value of acceleration and angular acceleration and therefore increasing the experimental value of I.
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