# Compound Pendulum & Torsion Pendulum  Item no.: F12

##### Introduction

Base on Newton’s second law and energy conservation, we will forward torque and rotational theory to study harmonic motions in reversal compound pendulum and torsion pendulum, which have been widely used in practical application such as torsion or pendulum clocks, crank system of engine, mechanical pressure gage, damping device and rotary flow meter etc.

##### Objectives
1. Compound pendulum the magnitude of gravity acceleration.
2. Torsion pendulum the stiffness coefficient of metal wire.
##### Experiment—Torsion pendulum

A torsion pendulum, in Fig.a ~ Fig.b, is made up by a circular disk of mass M suspended at a copper wire of length L. Here the smaller periodic oscillation will be induced while the distortion of material’s stiffness recovers from the torque subjected.

Here I0 indicates disk- rotating moment of inertia and I1, means the total rotating moment of inertia if additional circular shell is co-axially positioned above. Base on the oscillating period of rotation T, material stiffness coefficient n might be determined.

##### Experiment—Compound pendulum

Consider a mechanism of compound pendulum as the sketch below. Here both nuts, taken as rotating pivot by turn, might be screwed on the pendulum, in which one is fixed and the other might be regulated. Thus both corresponding periodic profiles of T1 and T2 , resulted from the exchange of rotating shaft, could be accessed. While survey the equilibrant period T1=T2 as setting the moving nut at appropriate situation, the maximum value of l1+ l2( the addition of distance from mass center to individual rotating axis) coupling with corresponding period T will be used to precisely predict the magnitude of gravity acceleration. That is the working principle of so called” inverted pendulum (another style of compound pendulum) ” proposed in this experiment.

1. 扭擺
2. 複擺
##### 實驗器材：
1. 鋁製實驗平台 x1
2. 直立支架 x1
3. 複擺 x1
4. 扭擺待測金屬線 x5 – 同長度同直徑金屬線：sk鋼/合金鋁/黃銅（直徑2mm、長度500mm）、同長度不同直徑金屬線：sk鋼（直徑2mm/1.5mm/1mm、長度500mm）
5. 轉動慣量測量體 x2 – 金屬圓盤、金屬圓環
6. 水平儀 x1
7. 內六角板手 x1