In the experiment, the hanging weight and the disk are released from rest, and we measure the final speeds as the hanging weight reaches the floor. h is the height of the hanging weight measured from the ground. I disk is the moment of inertia of the disk, and ω is the angular speed. (6) In this equation, m H is the mass of the hanging weight, and v its speed. Now the conservation of mechanical energy can be generalized to the rotational systems as: If there are only “conservative” forces acting on the system, the total mechanical energy is conserved. Ω is the angular speed in the unit of “radian”. It is expressed in an analogous form as the linear kinetic energy as follows: Therefore, it is not surprising to recognize that a rotational system also has rotational kinetic energy associated with it. As noted before, kinetic energy is the energy expressed through the motions of objects. In an earlier lab, we have considered the mechanical energy in terms of the potential and kinetic energy in the linear kinematics. Conservation of Mechanical Energy in Rotational Systems Spinning objects of different shapes can also be determined experimentally in the same way. 1 Schematic of the system of the spinning disk and dropping weight. Considering the hanging mass ( m H), the analysis from the free-body-diagram tells us that τ = rT = I disk α, (1) where I is the moment of inertia of the disk, r is the radius of the multi-step pulley on the rotary motion sensor and T is the tension on the string. Considering the rotational part of the system (taking a disk as an example) and ignoring the frictional torque from the axle, we have the following equation from Newton’s second law of motion. 1 shows a schematic of the experimental setup that you will use to experimentally determine the moment of inertia of the spinning platter. The table below summarizes the equations for computing “ I” of objects of some common geometrical shapes.ġ558 Experimental Determination of the Moment of Inertiaįig. “ I” is defined as the ratio of the “torque” ( τ ) to the angular acceleration ( α ) and appears in Newton’s second law of motion for rotational motion as follows:įor objects with simple geometrical shapes, it is possible to calculate their moments of inertia with the assistance of calculus. This lab extends the exploration of the Newtonian Mechanics to rotational motion.Īnalogous to the “mass” in translational motion, the “moment of inertia”, I, describes how difficult it is to change an object’s rotational motion specifically speaking, the angular velocity. The rotary motion kit (shown on the right) a LabPro unit a smart pulley (SP) string a mass holder and a set of masses a plastic ruler and a meter stick a digital caliper ACCULAB VI-1200 mass scale. In this lab, the physical nature of the moment of inertia and the conservation law of mechanical energy involving rotational motion will be examined and tested experimentally. International Journal of Scientific & Engineering Research, Volume 5, Issue 7, July-2014
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