Moment of Inertia free essay sample

To use a centripetal force apparatus to calculate the moment of inertia of rotating weights, using theories derived from ideas of energy transfer (Im = MR2 (g/2h)(t2-t02)) and point mass appoximation (m1r12 + m2r22). Set Up Procedure First we measured the weights of two masses and wingnuts that secure them. Then we placed one of the masses on the very end of a horizontal rod on the centripetal force apparatus, 0. 162 m away from the centre of the rod, and the other mass 0. 15 m away from the centre of the rod. Then we attached a 0. 2 kg mass to the bottom of a string and wound the string around the vertical shaft of the apparatus, so that the bottom of the weight rose to the bottom edge of the tabletop the apparatus was on. We measured the distance from the bottom of the weight to the floor, and then let the weight fall to the floor, and measured the time it took to do so. We will write a custom essay sample on Moment of Inertia or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page We repeated this measurement, using the same initial height, four more times. Then we took the masses and the wingnuts off the horizontal rod and let the 0. kg mass fall in the same way as before, five times. Then we replaced the masses and the wingnuts, but put them both on the edges of the horizontal rod, and repeated the same falling mass measurements five times. We moved the masses in towards the centre of the rod and continued to repeat the falling mass measurements. We moved the masses in toward the centre four more times, each time taking five falling mass measurements. Error in this part of the experiment could have come from improper estimation of time due to ambiguity in the falling mass. Our falling mass hung crookedly from its string, meaning their could have been variability in what was observed to be the starting and ending places of the fall, depending on where one decided to count as the place on the mass needing to touch the floor or pass the starting point, in order to consider the fall ended or begun. However, the errors didn’t really seem to affect this section of the experiment: we still ended up with the same moment of inertia in both methods of calculating it. Second Pass: The graph of Im vs. r2 shows 2 of the data points lying on a linear least square fit line, and the others laying close, but not within r2 error. It is possible that with Im error, the points would lie on the line, especially since they don’t lie far away. The line seems to be the best representation of the relationship between Im and r2, therefore, it can be said that the relationship defined in the equation Im = m1r12 + m2r22 is verified. In the graph of Im vs. r2, considering that r1 = r2, and m1 = m2, the slope represents Im/r2 = 2m. The slope is 0. 1223 kg, and 2m is 0. 1232 kg. The quantities are . 0009 kg apart, which seems reasonably within error, but could be verified through finding ? Im/r2. But considering the closeness in the amounts, and the fact that the graph verifies a linear relationship between the moment of inertia and the radius of the circle the masses make when turning, the point mass approximation seems a pretty good tool to use to estimate Im. In this part of the experiment, error could have come from, like in the first part, ambiguity in the falling mass. It could also have come from improper placement of m1 and m2 to each other: if they were not evenly spaced from the centre of the tool, it could have changed the time measurements. These two sources of error could be the reason why some of the data did not lie exactly on the line of best fit on the graph. Conclusion Our experimental data from the first pass showed that using formulas derived from ideas of energy conservation and point-mass approximation are equally valid. The second pass verified the pointmass approximation relationship between. Error did not affect our results hugely, but it makes some assertions less concrete: not all of our data points lay on our line that affirms the relationship between Im and r2, and while our graphical measurement of 2m was close to the experimental result, it was not exact. Some of the error in this part of the experiment probably carried over from the first part, in that we used the t0 data from that part, and that came from a crookedly hung mass; this experiment shows that errors can follow you from one part of the experiment to another, so at all times it is best to be careful, even when at first it doesn’t seem to affect the data.