![]() Check the extent to which the pulleys are circular and use an average radius. Obtain precise values for the diameters of the torque pulleys by measuring them using the callipers supplied. Section 1: comparing the theoretical value of aluminium disc and ring with that experimentally observed The pair of brass weights on a long thin rod. The opposite is true if the skater contracts arms.Ħ. Since KE is proportional to (angular velocity) ^2, and angular momentum is proportional to (angular velocity), KE decreases as her muscles do negative work. Therefore, angular velocity must decrease as a result. When a skater spreads her arms, rotational inertia increases while angular momentum is held constant. Lab script Question: How do figure skaters vary their moment of inertia, and why? Show that, if the angular momentum of the figure skater is conserved, varying the moment of inertia requires changing their kinetic energy. We applied parallel and perpendicular axis theorems to get the moment of inertia theoretically and then compared theoretical value with that experimentally observed. In the final section we examine factors which contribute to the moment of inertia. ![]() The second section involves investigation of the conservation of angular momentum, in which we drop a metal ring on an aluminium disc. The experiment is in three sections: the first section entails measuring the moment of inertia of a metal disc, comparing the theoretical value with that experimentally observed. The aim of experiments is to investigate a number of different aspects of rotational dynamics using an apparatus consisting of a set of rotating masses, a low friction bearing with an optical encoder connected to a PC, and a pulley system to accelerate the rotating masses with known torques. Physics Nobel Prize Winner MIT Prof Frank Wilczek on String Theory, Gravitation, Newton & Big Bang We can integrate Iz =integral and plug in ρ=constant for a uniform disk, we get Iz =1/2 MR^2ĭerivation of parallel axis theorem and perpendicular axis theorem from Wikipedia Experiments Using the above definitions, we can derive other formulas needed. Thus, J is conserved in the absence of applied torques.įor an isolated rigid body rotating at angular velocity ω rad/s about a fixed axis the z-component of J may be written: (where Γ is the torque resulting from the applied forces Fi) – the rotational equivalent of Newton’s (where vi is the velocity of each element) and its rate of change is given by: If we consider the origin to lie somewhere along the axis of rotation, the angular Relative positions are fixed and whose absolute positions measured with respect to an origin fixed in Particle Physics : The Future of Particle Physics Lies In Space Particle Physics : The Future of Particle Physics Lies In Space IntroductionĬonsider a rigid body to consist of a large number N of small mass elements of mass mi whose For all three experiments our theoretical values compare well with quantities experimentally determined as corresponding quantities differ by no more than 2 standard deviations. Then we plotted an inertia vs radius diagram and verified the theoretical prediction. In the third experiment we used parallel and perpendicular axis theorems to derive the moment of inertia of a rod connected with two bells. Using the moment of inertia previously determined to can calculate the total angular momentum before and after the collision, and they are found to be J-before 2.56+/-0.01e-3 kgm^2s^-1, and 2.54+/-0.01e-3 kgm^2s^-1 respectively for one set of data. In the second experiment we dropped the ring on the disc. From the experiment, the moment of inertia for the ring is 4.9+/- 0.1×10^-4 kg m^2, which matches well our theoretical value 5.00☐.03e-4kgm^2. Then we repeated the procedure by putting the ring above the disc to obtain the moment of inertia for the ring. By recording its angular displacement with respect to time we experimentally determined its moment of inertia, and then we compared this value with its theoretical value given by I=MR^2. ![]() In the first experiment we applied a torque on an aluminium disk. We have verified several key concepts in rotational dynamics: conservation of angular momentum, calculation of moment of inertia, and parallel axis theorem. While this report doesn’t derive everything from scratch, we started with several definitions and verified that the theoretical framework indeed describes physical reality by conducting experiments. ![]() Rotational Dynamics : An Investigation Abstract: Every theorem in rotational dynamics can be derived from corresponding linear dynamics equations if variables are properly defined.
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