Moment of inertia measured by three-wire pendulum

School of Electronics & Applied Physics, Hefei University of Technology

1. Master the principles and method of the moment of inertia measured by three-wire pendulum

2. Master the correct method of measuring the length, the quality and the time

3. Learn to use the three-wire pendulum to measure the moment of inertia of disk and ring round the axis of symmetry

4. Test Parallel axis theorem of the moment of inertia

Purpose of the experiment

Instruments of experiment Three-wire pendulum, bubble level, steel

tape measure, stopwatch, tested ring, cylinder under test

Experimental principle Three-wire pendulum are

constituted of the two disc A and B, both with uniform quality. With three lines which length is equal, B is hanging on the disc A. Three hanging points of each disc were connected to be an equilateral triangle which is inscribed circle. Shown in figure 1.

When objects on disk and the disk rotating around the axis of symmetry, measure the moment of inertia with a three-disc, the formula is

I=(mRrgT²)/(4I=(mRrgT²)/(4²H)²H) In the formula: m is the quality, R is the radius

of the circumscribed circle constituted with the three hanging point of the up disc. r is the radius of the circumscribed circle constituted with the three hanging point of the down disc. T is the rotation of cycle of the down disc, H is the distance between the two disc.

II11=[(m+M)RrgT²]/(4=[(m+M)RrgT²]/(4²H)-I²H)-I0

M is the quality of the ring, the ring is placed as the figure 2

shown.

1.Measure the moment of inertia of the disc with a three-disc, the

formula is II00=(mRrgT²)/(4=(mRrgT²)/(4²H)²H) M is the quality of the disc

2.Measure the moment of inertia of the ring with a three-disc, the formula is

33 .Test the Parallel axis theorem of the moment of inertia, the formula is

IId d =0.5{[(m+2m=0.5{[(m+2m11)RrgT²]/(4)RrgT²]/(4²H)-I²H)-I00}} MM11 is the quality of the is the quality of the

cylindercylinder The cylinder is placed on The cylinder is placed on

the disc as the figure 3 the disc as the figure 3 shown.shown.

When the cylinder is When the cylinder is circling the axis of circling the axis of symmetry, the formula issymmetry, the formula is

IIdd=0.5m=0.5m11rr11²+m²+m11d²d²

The connect and steps of the experiment

1.Adjust the three-wire pendulum 2.Measure the parameters of the

instrument, they are l, R, r, rl, R, r, rmm, a, b, r, a, b, r11

3.Measure the moment of inertia of the disc

4.Measure the moment of inertia of the ring

5.Test the Parallel axis theorem of the moment of inertia

Difficulty and Solution of the experiment 1.There are two kinds of instrument. Explain

clearly the respective 2.The rotation angle of the disc can not be too

much, because there is an assumptions that the rotation angle is small in the a derivative process.

3.The rotation system must be symmetrical.