理論力學(xué)轉(zhuǎn)動慣量實驗報告

理論力學(xué)轉(zhuǎn)動慣量實驗報告

【實驗概述】轉(zhuǎn)動慣量是描述剛體轉(zhuǎn)動中慣性大小的物理量，它與剛體的質(zhì)量分布及轉(zhuǎn)軸位置有關(guān)。正確測定物體的轉(zhuǎn)動慣量，對于了解物體轉(zhuǎn)動規(guī)律，機械設(shè)計制造有著非常重要的意義。然而在實際工作中，大多數(shù)物體的幾何形狀都是不規(guī)則的，難以直接用理論公式算出其轉(zhuǎn)動慣量，只能借助于實驗的方法來實現(xiàn)。因此，在工程技術(shù)中，用實驗的方法來測定物體的轉(zhuǎn)動慣量就有著十分重要的意義。IM-2剛體轉(zhuǎn)動慣量實驗儀，應(yīng)用霍爾開關(guān)傳感器結(jié)合計數(shù)計時多功能毫秒儀自動記錄剛體在一定轉(zhuǎn)矩作用下，轉(zhuǎn)過π角位移的時刻，測定剛體轉(zhuǎn)動時的角加速度和剛體的轉(zhuǎn)動慣量。因此本實驗提供了一種測量剛體轉(zhuǎn)動慣量的新方法，實驗思路新穎、科學(xué)，測量數(shù)據(jù)精確，儀器結(jié)構(gòu)合理，維護簡單方便，是開展研究型實驗教學(xué)的新儀器。【實驗?zāi)康摹?.

了解多功能計數(shù)計時毫秒儀實時測量（時間）的基本方法

2.

用剛體轉(zhuǎn)動法測定物體的轉(zhuǎn)動慣量3.

驗證剛體轉(zhuǎn)動的平行軸定理

4.

驗證剛體的轉(zhuǎn)動慣量與外力矩?zé)o關(guān)【實驗原理】轉(zhuǎn)動力矩、轉(zhuǎn)動慣量和角加速度關(guān)系系統(tǒng)在外力矩作用下的運動方程T×r+Mμ=Jβ2（1）由牛頓第二定律可知，砝碼下落時的運動方程為：mg-T=ma即繩子的張力T=m(g-rβ2)砝碼與系統(tǒng)脫離后的運動方程Mμ=Jβ1（2）由方程（1）（2）可得J=mr(g-rβ2)/(β2-β1)（3）角加速度的測量θ=ω0t+?βt2（4）若在t1、t2時刻測得角位移θ1、θ2則θ1=ω0t1+?βt2（5）θ2=ω0t2+?βt2（6）所以，由方程（5）、（6）可得β=2（θ2t1-θ1t2）/t1t2（t2-t1）【實驗儀器】3.驗證平行軸定理（圓柱體直徑38mm質(zhì)量2×400g）（1）D=40mm數(shù)據(jù)12345數(shù)據(jù)12345∏2.0451。8101.5201.8731.77911∏8.3928.0627.6328.1888.0452∏3.1622.8982.5382.9722.86012∏8.8038.4728.0408.6008.4573∏4.0293.7453.3533.8283.70713∏9.2068.8758.4449.0078.8624∏4.7664.4684.0614.5614.43214∏9.6149.2828.8519.4179.2725∏5.4125.1064.6895.2055.07215∏10.0199.6879.2569.8269.6806∏6.0005.6875.2665.7935.65716∏10.42910.0969.66510.23810.0917∏6.5386.2215.7966.3316.19417∏10.83710.50410.07310.64910.5018∏7.0436.7226.2956.8376.69018∏11.24810.91510.48411.06310.9159∏7.5157.1916.7637.3107.17019∏11.65811.32410.89411.47611.32710∏7.9667.6397.2097.7617.61920∏12.07111.73711.30711.89311.743數(shù)據(jù)處理第一組第二組第三組第四組第五組平均值β1-0.03476-0.03488-0.03880-0.03030-0.02600-0.03309β20.81840.82360.80510.80950.81100.8135轉(zhuǎn)動慣量0.0015270.0013840.0017780.0018900.0019510.001706實測值：0.0008530百分誤差19.80%理論值：0.0007120（2）D=80mm數(shù)據(jù)12345數(shù)據(jù)12345∏2.1141.7222.2531.9611.77111∏8.9948.3919.1408.8698.4942∏3.3352.8473.4643.1482.91212∏9.4228.8359.5889.3238.9403∏4.2593.7434.3994.0813.81513∏9.8849.27410.0299.7719.3794∏5.0514.5165.1964.8824.59414∏10.3299.71610.47410.2239.8225∏5.7495.1985.8985.5585.28315∏10.77310.15710.91710.67310.2636∏6.3885.8256.5376.2345.91316∏11.22110.60211.36411.12710.7087∏6.9746.4007.1236.8266.49217∏11.66811.04611.81011.57911.1528∏7.5256.9417.6727.3817.03618∏12.11811.49312.25912.03511.5999∏8.0407.4488.1867.9027.45619∏12.56711.93912.70712.49012.04510∏8.5317.9928.6768.3898.03320∏13.01912.38913.15912.94812.495數(shù)據(jù)處理第一組第二組第三組第四組第五組平均值β1-0.03247-0.03681-0.02669-0.02270-0.02706-0.02902β20.69240.69260.69360.66520.68600.6860轉(zhuǎn)動慣量0.0057500.0056040.0059230.0062040.0061970.005936實測值：0.002968百分誤差12.77%理論值：0.002632（3）D=120mm數(shù)據(jù)12345數(shù)據(jù)12345∏2.1762.3272.1892.5032.49111∏9.7609.9549.75510.18710.2342∏3.4833.6513.4923.8533.85712∏10.25810.45210.25210.68710.7323∏4.5084.6824.5134.8954.91413∏10.74810.94310.74211.17911.2234∏5.3875.5645.3905.7865.81314∏11.24211.43811.23611.67611.7185∏6.1626.3246.1636.5686.60215∏11.73511.93111.72812.17112.2126∏6.8707.0526.8707.2827.32116∏12.23212.42812.22512.67112.7097∏7.5197.7047.5197.9357.97917∏12.72812.92412.72013.16913.2058∏8.1298.3168.1288.5488.59518∏13.22813.42413.21913.67113.7059∏8.7008.8908.6979.1229.16919∏13.72613.92213.71714.17114.20310∏9.2449.4369.2419.6699.71620∏14.22814.42414.21914.67614.706數(shù)據(jù)處理第一組第二組第三組第四組第五組平均值β1-0.02348-0.01940-0.02382-0.02254-0.01723-0.02195β20.55430.55700.55720.55700.56770.5546轉(zhuǎn)動慣量0.012730.012820.012560.012470.013520.01282實測值：0.01282百分誤差9.85%理論值：0.011674.驗證轉(zhuǎn)動慣量與外力矩?zé)o關(guān)塔輪半徑r=50mm數(shù)據(jù)12345數(shù)據(jù)12345∏1.2581.4771.3671.3151.23011∏6.5206.8846.7396.6386.4782∏2.1192.3972.2662.1992.08612∏6.9147.2797.1347.0326.8723∏2.8143.1232.9842.9082.77813∏7.3077.6377.5287.4247.2654∏3.4183.7483.6053.5223.38114∏7.7038.0707.9267.8207.6615∏3.9564.2984.1544.0673.91715∏8.0988.4658.3218.2148.0556∏4.4504.8004.6564.5644.41116∏8.4968.8648.7208.6128.4537∏4.9055.2615.1165.0214.86517∏8.8939.2619.1189.0088.8498∏5.3345.6945.5485.4525.29318∏9.2939.6629.5199.4079.2499∏5.7366.0995.9535.8555.69519∏9.69110.0619.9199.8059.64810∏6.1296.4926.3466.2476.08720∏10.09310.46310.32210.20710.050數(shù)據(jù)處理第一組第二組第三組第四組第五組平均值β2-0.04709-0.04261-0.04674-0.04727-0.04293-0.04533β11.08401.09161.07071.07891.08071.0811轉(zhuǎn)動慣量0.021590.021530.021850.021680.021730.02168誤差：2.25%由此可知：在誤差范圍內(nèi)，剛體轉(zhuǎn)動慣量與外力矩?zé)o關(guān)【誤差