2023年轉(zhuǎn)動(dòng)憒量的測(cè)定實(shí)驗(yàn)報(bào)告2023年轉(zhuǎn)動(dòng)憒量的測(cè)定實(shí)驗(yàn)掖告實(shí)驗(yàn)小組成員：實(shí)驗(yàn)時(shí)間：2018年5月18日18:00一一19:30實(shí)驗(yàn)地點(diǎn):同濟(jì)大學(xué)四平路校區(qū)力學(xué)實(shí)驗(yàn)中心【實(shí)驗(yàn)?zāi)康摹?了解多功能計(jì)數(shù)計(jì)時(shí)亳秒儀實(shí)時(shí)測(cè)吊(時(shí)間)的基本方法.用剛體轉(zhuǎn)動(dòng)法測(cè)定物體的轉(zhuǎn)動(dòng)慣量.驗(yàn)證剛體轉(zhuǎn)動(dòng)的平行軸定理.驗(yàn)證剛體的轉(zhuǎn)動(dòng)慣量與外力矩?zé)o關(guān)【實(shí)驗(yàn)原理】.轉(zhuǎn)動(dòng)力矩、轉(zhuǎn)動(dòng)慣量和角加速度關(guān)系系統(tǒng)在外力矩作用下的運(yùn)動(dòng)方程(1)由牛頓第二定律可知，祛碼下落時(shí)的運(yùn)動(dòng)方程為：mg-T=ma即繩子的張力T=m(g—rP2)祛碼與系統(tǒng)脫離后的運(yùn)動(dòng)方程TOC\o"1-5"\h\zMu=J61(2)由方程(1)(2)可得J=mr(g-rB2)/(B2-8i)(3).角加速度的測(cè)量o=30t+%Bt2(4)若在t1、t2時(shí)刻測(cè)得角位移01、02則01=GO0ti+%81202=00t2+/4Pt2（6）所以，由方程（5）、（6）可得B=2（02tl-01t2）/t1t2（t2-tl）【實(shí)驗(yàn)儀器】1、IM—2剛體轉(zhuǎn)動(dòng)慣量實(shí)驗(yàn)儀（含霍爾開(kāi)關(guān)傳感器、計(jì)數(shù)計(jì)時(shí)多功能亳秒儀、一根細(xì)繩、一個(gè)質(zhì)量為100g的跌碼等，塔輪直徑從下至上分別為30mm、40mm、50mm>60mm,載物臺(tái)上的孔中心與圓盤(pán)中心的距高分別為40mm、80mm、120mm）2、一個(gè)鋼質(zhì)圓環(huán)（內(nèi)徑為175mm,外徑為215mm，質(zhì)量為995g）3、兩個(gè)鋼質(zhì)圓柱（直徑為38mm，質(zhì)量為400g）【實(shí)驗(yàn)環(huán)節(jié)】.實(shí)驗(yàn)準(zhǔn)備在桌面上放置IM-2轉(zhuǎn)動(dòng)慣量實(shí)驗(yàn)儀，并運(yùn)用基座上的三顆調(diào)平螺釘，將儀器調(diào)平。將滑輪支架固定在實(shí)驗(yàn)臺(tái)面邊沿,調(diào)整滑輪高度及方位，使滑輪槽與選取的繞線(xiàn)塔輪槽等高,且其方位互相垂直。通用電腦計(jì)時(shí)器上光電門(mén)的開(kāi)關(guān)應(yīng)接通，另一-路斷開(kāi)作備用。當(dāng)用于本實(shí)驗(yàn)時(shí)，設(shè)立1個(gè)光電脈沖記數(shù)1次，1次測(cè)量記錄大約20組數(shù)。.測(cè)量并計(jì)算實(shí)驗(yàn)臺(tái)的轉(zhuǎn)動(dòng)慣最1）放置儀器，滑輪置于實(shí)驗(yàn)臺(tái)外3-4cm處，調(diào)節(jié)儀器水平。設(shè)立亳秒儀計(jì)數(shù)次數(shù)為20。2）連接傳感器與計(jì)數(shù)計(jì)時(shí)毫秒儀,調(diào)節(jié)霍爾開(kāi)關(guān)與磁鋼間距為0.4-0.6cm,轉(zhuǎn)離磁鋼，復(fù)位亳秒儀，轉(zhuǎn)動(dòng)到磁鋼與霍爾開(kāi)關(guān)相對(duì)時(shí)，毫秒儀低電平指示燈亮，開(kāi)始計(jì)時(shí)和計(jì)數(shù)。3）將質(zhì)量為m=100g的祛碼的?端打結(jié)，沿塔輪.上開(kāi)的細(xì)縫塞入,并整齊地繞于半徑為r的塔輪。4）調(diào)節(jié)滑輪的方向和高度，使掛線(xiàn)與繞線(xiàn)塔輪相切，掛線(xiàn)與繞線(xiàn)輪的中間呈水平。5）釋放祛碼,跌碼在重力作用下帶動(dòng)轉(zhuǎn)動(dòng)體系做加速度轉(zhuǎn)動(dòng)。6）計(jì)數(shù)計(jì)時(shí)亳秒儀自動(dòng)記錄系統(tǒng)從0n開(kāi)始作1"，2n……角位移相相應(yīng)的時(shí)刻。.測(cè)量并計(jì)算實(shí)驗(yàn)臺(tái)放上試樣后的轉(zhuǎn)動(dòng)慣量將待測(cè)試樣放上載物臺(tái)并使試樣幾何中心軸與轉(zhuǎn)動(dòng)軸中心重合，按與測(cè)量空實(shí)驗(yàn)臺(tái)轉(zhuǎn)動(dòng)慣量同樣的方法可分別測(cè)量跌碼作用下的角加速度B2與祛碼脫離后的角加速度B1,由⑶式可計(jì)算實(shí)驗(yàn)臺(tái)放上試樣后的轉(zhuǎn)動(dòng)慣量J，再減去實(shí)驗(yàn)環(huán)節(jié)2中算得的空實(shí)驗(yàn)臺(tái)轉(zhuǎn)動(dòng)慣量即可得到所測(cè)試樣的轉(zhuǎn)動(dòng)慣量。將該測(cè)量值與理論值比較，計(jì)算測(cè)量值的相對(duì)誤差。.驗(yàn)證平行軸定理將兩圓柱體對(duì)稱(chēng)插入載物臺(tái)匕與中心距離為d的圓孔中，測(cè)量并計(jì)算兩圓柱體在此位置的轉(zhuǎn)動(dòng)慣量，將測(cè)量值與理論計(jì)算值比較，計(jì)算測(cè)量值的相對(duì)誤差。.驗(yàn)證剛體定軸轉(zhuǎn)動(dòng)慣量與外力矩?zé)o關(guān)通過(guò)改變塔輪直徑對(duì)轉(zhuǎn)盤(pán)施加不同的外力矩，測(cè)定在不同外力矩下轉(zhuǎn)盤(pán)的轉(zhuǎn)動(dòng)慣量，與理論值進(jìn)行比較，在一定允許的誤差范圍內(nèi)驗(yàn)證結(jié)論?！緦?shí)驗(yàn)數(shù)據(jù)與解決】.測(cè)量空盤(pán)的轉(zhuǎn)動(dòng)慣量塔輪半徑r=40mm祛碼100g

數(shù)據(jù)第一組第二組第三組數(shù)據(jù)第一組第二組第三組1n1.1351.7821.2081in6.7167.8916.8812n1.9942.8242.09912n7.1478.3417.3163n2.2703.6472.84013n7.5818.7937.7524丸3.3554.3463.48814n8.0149.2448.1895n3.9324.9684.07215n8.4509.6988.6276兀4.4615.5314.60816n8.88510.1529.0667K4.9556.0525.10617Ji9.32310.6089.5078n5.4176.5375.57318Ji9.76011.0649.9489jt5.8556.9946.01419n10.20011.52310.39010Ji6.2857.4416.44720n10.64011.98110.833數(shù)據(jù)解決第一組第二組第三組平均值131-0.03767-0.04478-0.03896-0.04187B20.3098020.8718310.8712370.871534轉(zhuǎn)動(dòng)慣量0.0563720.0213450.0214950.02142（注：計(jì)算平均值時(shí)舍去第一組的壞值）.測(cè)量圓環(huán)的轉(zhuǎn)動(dòng)慣量塔輪半徑r=40mm圓環(huán)外徑215mm內(nèi)徑175mm質(zhì)量995g數(shù)據(jù)第一組第二組第三組數(shù)據(jù)第一組第二組第三組1n1.6922.2701.86111n8.7999.7269.1362n2.8513.4863.08312n9.33410.3069.6793jt3.7934.4874.04913n9.87110.88710.2194n4.6065.3384.88614n10.40811.47010.7655n5.3346.0925.62515n10.94812.05511.3076Ji5.9996.7776.30416Ji11.48812.64211.8567n6.6157.4086.92617n12.03013.23012.4018n7.1907.9967.51218Ji12.57313.82012.9539n7.7338.5718.05919n13.11714.41213.50110n8.2659.1488.59920n13.66315.00514.056數(shù)據(jù)解決第一組第二組第三組平均值Bl-0.02810.01449-0.02165-0.02141B20.5956490.5944040.5872090.592421J盤(pán)+環(huán)0.0313460.0321110.0321140.031857J環(huán)0.0103460.0111110.0111140.010857環(huán)的轉(zhuǎn)動(dòng)慣量理論值為0.009702,誤差為11.9%.驗(yàn)證平行軸定理（圓柱體直徑38mm質(zhì)量2X400g）（1）D=40mm數(shù)據(jù)第一組第二組第三組數(shù)據(jù)第一組第二組第三組

圓柱轉(zhuǎn)動(dòng)慣量理論值為0.0014244,百分誤差為54.51%1n1.3411.5331.49611n7.5167.8937.6362jt2.2992.5512.51012n8.0308.4188.0983n3.0863.3703.32213n8.5478.9448.5574n3.7724.0764.02914n9.0659.4739.0215jt4.3874.7064.65515n9.58410.0039.4826n4.9505.2815.23016jt10.10610.5359.9487n5.4725.8115.75817n10,62811.06910.4128n5.9816.3296.25618n11.15311.60510.8819n6.4916.8496.72119n11.67912.14311.34710Ji7.0037.3707.18020n12.20712.68211.819數(shù)據(jù)解決第一組第二組第三組平均值B1-0.03732-0.03802-0.03044-0.03526320.8085470.808220.803620.806795J盤(pán)+圓柱0.0230950.0230850.0234230.023201J圓柱0.0020950.0020850.0024230.002201(2)D=80mm

數(shù)據(jù)第一組第二組第三組數(shù)據(jù)第一組第二組第三組1n1.5421.2951.50711n8.1867.6608.0522n2.6082.2662.57012n8.7118.1278.5493n3.4783.0883.43013n9.2388.6909.0434n4.2303.8044.18214n9.7679.2059.5435n4.9034.4554.8515n10.2979.72710.046n5.5175.0496.46616n10.82910.24510.5437n6.0865.6066.03217jt11.36310.77011.0438n6.6196.1256.56718n11.89811.29111.5499n7.1406.6377.06619n12.43611.81912.05110n7.6627.1457.5620n12.97412.34412.56數(shù)據(jù)解決第一組第二組第三組平均值31-0.02111-0.0757-0.03212-0.04298B20.6929340.6944560.1102420.49921J盤(pán)+圓柱0.0273720.02530.13760.0360771976J圓柱0.0063720.0043770.1166190.005374圓柱轉(zhuǎn)動(dòng)慣審理論值為0.0052644,百分誤差為2.09%(3)D=120mm圓柱轉(zhuǎn)動(dòng)慣量理論值為0.01167,百分誤差為9.73%數(shù)據(jù)第一組第二組第三組數(shù)據(jù)第一組第二組第三組1H2.0751.9751.93611H9.6479.4979.4212兀3.3613.2403.19212n10.20910.0599.9803H4.3724.2404.18613n10.76810.61710.5364n5.2445.1065.04714n11.33311.18311.0985JT6.0115.8695.80715n11.89511.74511.6566H6.7156.5706.50616n12.46412,31412.2227n7.3607.2137.14617Ji13.02912.87912.7848n7.9677.8187.74918n13.60113.45113.3529n8.5338.3838.31219n14.17014.01913.918lOn9.0928.9428.86920Ji14.74514.59414.490數(shù)據(jù)解決第一組第二組第三組平均值Bl0.023640.023640.02162-0.02297320.5557310.5544050.5564050.555514J盤(pán)+圓柱0.0337530.033830.0338320.033805J圓柱0.0127530.012830.0128320.012805根據(jù)己知數(shù)據(jù)可以計(jì)算出通過(guò)圓柱體對(duì)稱(chēng)軸的轉(zhuǎn)動(dòng)慣量為J0R.00288.由之前的計(jì)算結(jié)果可以當(dāng)D=40mm,J=0.00220233,因此可以計(jì)算得J+MD-2=0.000288根據(jù)圓柱體的轉(zhuǎn)動(dòng)慣量公式，計(jì)算其理論值為0.000221誤差為2.4%,在誤差范圍內(nèi)，因此可以驗(yàn)證平行軸定理

4.驗(yàn)證轉(zhuǎn)動(dòng)慣量與外力矩?zé)o關(guān)塔輪半徑r=50mm數(shù)據(jù)第一組第二組第三組數(shù)據(jù)第一組第二組第三組1冗1.0431.5151.09311完6.2297.1176.3572311.8322.4431.90412n6.6667.5736.7983n2.4853.1692.57013it7.1008.0267.2364冗3.0633.7953.15814n7.5398.4847.6795JT3.5804.3453.68115Ji7.9748.9398.1196兀4.0594.8504.16516幾8.4159.4008.5647冗4.5005.3124.61117?8.8539.8579.0078元4.9335.7635.04818n9.29610.3209.454