三线摆测量刚体转动惯量-实验报告VIP专享VIP免费

UniversityofScienceandTechnologyofChina96JinzhaiRoad,HefeiAnhui230026,ThePeople'sRepublicofChina三线摆测量刚体转动惯量实验报告李方勇PB052102840510第29组2号（周五下午）2006.11.06实验题目三线摆测量刚体转动惯量实验目的1、掌握用三线摆测定物体的转动惯量的方法；2、验证转动惯量的平行轴定理；3、根据误差公式及实际装置、仪器情况、合理选择仪器和安排测量。实验仪器三线摆，电子秒表，游标卡尺，米尺，水准仪，物理天平，待测的金属圆环和两个质量，形状相同的金属圆柱。实验原理图4—1三线摆结申18斛券技虑*事图4—2下圆盘的扭转振1．三在直角AA中：GA)=(AC)L=H2+(R-r)2,(4.1b)由AA知：GC)=(AO)+(OC)-2(AO)OC)COSa2222222222在直角AA中：(AA)=^AC)+(AC),(4.3a)2222即：R2+r2-2Rrcosa,(4.2)L=(H_h)2+R2+r2一2Rrcosa,(4.3b)比较式(4.1a)和(4.3b)得：h(H-h)=Rr(1-cosa).(4.4)把cosa按级数展开代入上式并消去小量得:Rra2h=—,(4.6)2H1(da21(dh'—I+—m—20Idt20*dt1201dt丿(da}201dt丿1■■—201dt丿(4.6)代入(4.9)并对t微分，得:d2amgRr=_oa,(4.10)dt2IH0该式为简谐振动方程,解得:mgRr①2=0^—IH0故有2+mgh=恒量,4.2．在圆盘上加上物体后：2+mgh=恒量,(4.8)(da\2机械能守恒得：1>>—mI=(mo+mgRrT2,(4.12)14兀2HigRrI=I一I=[(m+m)T2一mT2],(4.13)104兀2H01003．验证转动惯量的平行轴定理I=I+md2,(4.14)ac实验内容1.测定仪器常数R,r,H。2．测量下圆盘得转动惯量，并计算其误差。3．测量圆环得转动惯量并与理论值比较求相对误差4．验证平行轴定理。实验数据见另上交的纸质原始数据数据处理及分析评定实验结果的不确定度1．仪器常数平均值mean及A类不确定度UA由Origin处理而得Au=k仪B0.68C表4－1仪器常数单位mm123456meanUAUBU102.6102.6102.6102.6102.6102.6102.63330.00660.010.01R545123562451.3251.3251.3251.3051.3151.310.00330.010.01r50550551.316673220.13820.030.14H481.9481.0481.5481.7481.8481.3481.5333401170.0169.9169.9169.9169.9169.90.01110.010.01D内169.9667内082668626190.0190.0190.0190.0190.0190.00.00330.010.01D外190.0033外000200322沁、-0.15s估uu囂10伐)2+・)2+4(圆盘质量m°=360.3g圆环质量m环=397.5g圆柱质量m柱=200.0g2．时间测量电子秒表A估»A仪单位s12345meanUAUBU50T071.3171.1971.1471.1571.6571.2880.095410.0860.1284550T]82.8281.5882.3081.7481.8082.0480.227470.0860.2431850T2150.850.2850.43——50.503330.154520.0860.1768450T2253.1153.0853.18——53.123330.029630.0860.0909650T2357.9858.3958.30——58.223330.124410.0860.1512450T2466.7766.2766.34——66.460000.156310.0860.1784150T2576.8876.4376.5——76.603330.13980.0860.164133．求下圆盘的转动惯量1o--2505^（5OTo）2-1-9875X10一3畑m2不确定度：mgRrmgInI-In(50T)2-In』+InR+Inr+2ln(50T)-InH02500x4兀2H02500x4兀20dIdRdrd(50T)dH—0—++20———IRr50TH00uuuu(TT)2-(R)2+—)2+4(50J)2+2IRr50T0U50T)2+2-7.2x10—6kg-m2,p-0.6850T0.••I-(1.9875土0.0072)x10-3kg•m2,p-0.6804．求圆环的转动惯量B表4－2时间测量注T21〜T25分别为d=0〜80mm的周期gRu(m0+m)(50T)2—m0(50T0)2=(m+m)2(50T)u01(50T)一m(50T)2u00(50T0)u(m+m)(50T)2—m(50T)2u=II00I=[(m+m)(50T)2一m(50T)2]=3.3498x10-3kg-m22500x4兀2H010不确定度：/U、rr2+(—p.)2+[(m0+m)(50T)2—/"“©。珀)2]2+r(m+m)(50T)2—m(50T)20100I=(3.3498土0.0087)x10-3kg-m2,p=0.68圆环的转动惯量的理论值I=1m(D2+D)=3.2292x10-3kg-m2理8内外相对误差QI—I6=―理x100%=3.4%I理5．验证平行轴定理：(m+2m)gRrI=0柱T2a4兀2HI=I+2md2=(mD2+2mD2)+2md2理c柱80柱柱柱表4－3平行轴定理数据d(mm)50T(s)系统转动惯量I(x10—3kg-m2)a相对误差6实测值理论值050.503332.1049(I)c1.97766.4%2053.123332.25002.13765.3%4058.223332.79762.61766.8%6066.460003.64513.41766.6%8076.603334.84274.53766.7%2=8.7x10-6kg-m2,p=0.685g=209.71[2006-11-712:40"/Graph1(2454046)]LinearRegressionforData11_B:Y=A+B*XParametervalue...