The principle of measurement is to measure the rotation period, mass and other parameters of a rigid body, and then calculate the moment of inertia of the rigid body to be measured by using relevant formulas. A key step in this process is to measure the moment of inertia of an empty disk first, and then put the rigid body to be measured on the empty disk and measure the moment of inertia of both in the same way.
According to the superposition principle of the moment of inertia of rigid bodies, the moment of inertia of rigid bodies to be measured can be obtained by reducing the moment of inertia of empty disks. The verification of parallel axis theorem is also based on this. It is also necessary to measure the moment of inertia of the empty disk first, and then put two small cylinders with the same mass and the same geometric size on the empty disk.
Pay attention to the symmetrical placement (to be equipped in the cylinder experimental device), and then measure the moment of inertia of the two cylinders around the central axis. Because cylinders are regular rigid bodies, we can calculate their moment of inertia according to the formula, that is, the moment of inertia around the central axis, and measure the moment of inertia around the central axis and the distance from the cylinder to the center, so that we can verify the parallel axis theorem of the moment of inertia.
Calculation formula of measuring moment of inertia by three-line torsion pendulum method
The basic method is still to measure the moment of inertia J0 of the plate first, and then put the measured object on the plate to make the axes of the two coincide. If the moment of inertia J/ is the same as * *, then the moment of inertia of the measured object is J= J/ -J0. There are two situations in this measurement: one is that the axis of the measured object passes through its center of mass. In this case, it is only necessary to pay attention to the coincidence of the axis of the measured object and the axis of the triple pendulum.
On the other hand, the axis of rotation of the measured object does not pass through its center of mass. At this time, when the rotating shaft of the measured object coincides with the rotating shaft of the three-wire pendulum, the lower plate will be inclined (the stress on the three suspension wires will be uneven). In order to keep the lower plate level, the counterweight should be carried out according to the specific situation, and the lower plate level should be kept by the weight of the counterweight. Measure the total moment of inertia of the system, and then subtract the moment of inertia of the lower plate and the weight, which is the moment of inertia of the measured object.