How to measure the moment of inertia of an object with a three-line pendulum in college physics experiments: how to measure the moment of inertia of an arbitrary shape object around its center of mass? Write out the steps The structure of the three-line pendulum is shown in the figure. On the circumference of the upper disk, the trilinear pendulum is symmetrically connected to the vertex of the regular triangle at the edge of the larger uniform disk below along the vertex of the equilateral triangle.

When the three horizontal lines of the upper and lower plates are equal in length, the upper coil rotates by a small angle with the vertical central axis O 1O, and the suspended great circle twists around the central axis O 1O with the help of the tension of the suspension line.

The center of mass o of the footwall will rise and fall along the rotation axis, as shown in Figure 4.2.3-2. = h is the vertical distance between the centers of the upper and lower disks; = h is the height when the footwall vibrates; Is the radius of the upper wall; Is the radius of the footwall; α is the twist angle.

Extended data:

Experimental content

1, measuring instrument constant and:

Appropriate selection of measuring instruments and instruments to reduce measurement uncertainty. The experimental steps are designed by ourselves to ensure the level of the upper and lower disks of the three-wire placement, so that the instrument can achieve the best measurement state.

2. Measure the moment of inertia of the lower plate and calculate its uncertainty:

Rotate the small disk above the three-line pendulum to make it rotate around its own axis by an angle α, and twist the disk below with the help of the tension of the line to avoid shaking left and right. The measurement method is drawn up by ourselves, which makes the uncertainty of periodic measurement less than that of other measurement quantities. Using the formula (12), the uncertainty transfer formula is obtained, and the uncertainty is calculated.

3, measuring the moment of inertia of the ring:

Put the ring to be measured on the lower plate, and pay attention to make the center of mass of the ring just on the rotating shaft to measure the moment of inertia of the system. Measure the mass, inner diameter and outer diameter of the ring. Use equation (14) to find the moment of inertia of the ring. Compared with the theoretical value, the relative error is obtained.