Rotational Dynamics
In this experiment, the rotational motion of a solid pulley was studied. A mass was hung on a string, which was wrapped around the pulley. Using the mass hung on the string and accelerations given by a motion detector below the mass, the moment of inertia of the pulley can be discovered. This experiment showed that the average value for moment of inertia of the specific pulley was 0.00268 Kgm2 with an uncertainty of 0.00048 Kgm2. This same calculation was performed using the textbook definition for the moment of inertia of a solid disk. The given equation I=1/2MR2 , values for M and R were given and the resulting calculation produced a value for I of 0.00272 Kgm2 with uncertainty of 0.00015 Kgm2. The experiment showed that the values from both techniques of derivation come out to be the same value when the uncertainty is accounted for. In this experiment, the moment of inertia of a solid disk was studied. In particular, the forces needed to bring about a change in the rotational motion. For an extended object, a force acting anywhere away from the center of gravity will cause a rotation. This can be seen in the experiment because the force put on the pulley by the string is at a measurable d
(.050(9.8))-(.050(.619))=.459. After this, the torque can be determined by dividing the dynamic tension by the radius (.459/.076)=.0349. Finally, the moment of inertia can be calculated by taking the torque minus the frictional torque, then dividing that quantity by the angular acceleration (.0349-.015)/8.145=.00244. By doing each of these equations for the best case scenario, and also by using a possible set of values that are further away from the derived answer, uncertainty was calculated for the above set of calculations to be +/- .00029. Therefore, this value, which was derived through experimentation and many small calculations, ends up fitting into the expected value of 0.00272 Kgm2, when uncertainties are accounted for. In conclusion, the static determination of the moment of inertia based on its geometry was proven to be true. This value and the value for the moment of inertia of a solid disk were both calculated, and when the uncertainties were accounted for, the values overlapped. It seemed that the values from the experiment gave more accurate answers that those taken from the graph afterwards. The experimental value for moment of inertia of the disk was found to be 0.00268 Kgm2 with an uncertainty of 0.00048 Kgm2. The static determination was found to be 0.00272 Kgm2 with uncertainty of 0.00015 Kgm2.
Some common words found in the essay are:
Theory Torque, , moment inertia, falling mass, Linear Accel, pulley string, kgm2 uncertainty, Falling Mass, string wrapped pulley, 000272 kgm2 uncertainty, moment inertia pulley, object magnitude, inertia solid, uncertainty 000015, value 000272, 000272 kgm2, value 000272 kgm2, 000015 kgm2, mass hung string,
Approximate Word count = 1196
Approximate Pages = 5 (250 words per page double spaced)
|
