同济大学刚体转动惯量实验.docx

同济大学刚体转动惯量实验报告实验成员：*实验组别：第四组实验时间：2013.10.28实验地点：力学实验中心105一 实验目的1. 了解多功能计数计时毫秒仪实时测量（时间）的基本方法2. 用刚体转动法测定物体的转动惯量3. 验证刚体转动的平行轴定理4. 验证刚体的转动惯量与外力矩无关二 实验原理1. 转动力矩、转动惯量和角加速的关系系统在外力矩作用下的运动方程T*r+M=J2 (1)由牛顿第二定律可知，砝码下落时的运动方程为：mg-T=ma即绳子的张力T=m(g-r2)砝码与系统脱离后的运动方程：M=J1 （2）由方程（1）和方程（2）可得J=mr(g-r2)/(2-1)2. 角加速度的测量=0t+0.5t2若在t1、t2时刻测得角位移1和2，则1=0t1+0.5t122=0t2+0.5t22所以，有以上两方程可得=2（2t1-1t2）/t1t2(t2-t1)三 实验步骤1. 放置仪器，滑轮置于实验台外3-4cm,调节仪器水平，设置毫秒仪计数次数2. 连接传感器与计数计时毫秒仪，调节霍尔开关与磁钢间距为0.4-0.6cm,转离磁钢，复位毫秒仪，转动到磁钢与霍尔开关相对时，毫秒仪低电平指示灯亮，开始计时和技数3. 将质量为m=100g的砝码的一端打结，沿塔轮上开的细缝塞入，并整齐地绕于半径为r的塔轮4. 调节滑轮的方向和高度，使挂线与绕线塔轮相切，挂线与绕线轮的中间呈水平5. 释放砝码，带动转动体系做加速度转动6. 计数计时毫秒仪自动记录系统从0开始作1，2角位移相应的时刻四 实验装置计数计时毫秒仪、五 实验数据1转动次数（）空载40(直径）2011.05511.79211.07111.15311.13911.1131910.61611.34410.63210.71310.69910.6741810.17810.89710.19510.27410.26110.236179.74310.4539.7619.8379.8259.8169.30810.019.3279.4029.399.366158.8769.5698.8958.9698.9588.934148.4459.1298.4658.5368.5268.503138.0178.6928.0378.1068.0978.074127.5898.2567.6097.6777.6687.646117.1637.8227.1847.2517.2427.22106.7397.3896.766.8256.8176.79596.3036.9456.3256.3886.3816.3685.8446.4755.8665.9285.9215.975.35959785.385.4415.4355.41464.845.4444.8624.924.9154.89554.2834.8674.3044.364.3554.33643.6744.2323.6953.7473.7433.72532.9973.523.0183.0663.0623.04522.2222.6892.242.2822.2792.26411.2851.6461.2991.3291.3291.3162，t12.9983.2213.0053.0313.0263.022,t24.5594.8294.5674.5994.5924.5841,t11.2911.3181.291.2961.2931.2921,t23.0383.13.0343.0473.0423.03920.8094470.8112650.8106110.8105270.8121220.8132971-0.07057-0.06383-0.06624-0.06267-0.06847-0.06683J0.0222350.0223610.0223160.0224090.0222210.022232J0.0222732.转动次数（）圆环 175,215,936，砝码1002013.32313.37713.42613.42713.4031912.79712.84712.89712.89712.8741812.27212.31912.3712.26812.3471711.7511.79411.84611.84211.8231611.2311.2711.32411.31711.31510.71210.7510.80410.79610.7811410.19610.23110.28610.27610.262139.6839.7149.7719.7599.746129.1719.1999.2579.2439.232118.6628.6878.7468.738.72108.1548.1778.2358.2188.2197.6337.6527.7127.6947.68787.0837.0997.167.147.13576.5026.5146.5756.5546.55265.985.895.955.9275.92755.2115.2175.2765.2525.25544.4794.4824.5384.5124.51933.6643.6613.7153.6913.69822.7262.7192.7662.7492.75311.5861.581.611.6031.6052，t13.6253.6373.6663.6493.652,t25.4975.5195.555.5375.531,t11.5471.5561.5531.5581.5541,t23.643.6633.6553.6683.65720.5702110.5623910.5671790.5589190.5676461-0.04849-0.05072-0.04948-0.05104-0.04887J0.0316430.0319310.0317480.0320970.031755理论值0.031263实际值0.031835误差1.80%3.转动次数（）验证平行轴 40mm(半径）,400克2011.64811.47212.0511.45211.6241911.18911.01611.58610.99611.1661810.73110.56111.12310.54110.7091710.27510.10810.66310.08910.255169.8219.65710.2059.6389.802159.379.2099.7499.199.352148.928.7619.2948.7428.902138.4728.3168.8438.2988.456128.0267.8738.3927.8548.01117.5827.4327.9447.4137.567107.146.9927.4976.9747.12696.6876.5417.0396.5236.67286.2096.0666.5556.0486.19375.7025.5646.0425.5455.68765.1615.0275.4935.0095.14554.5794.454.8994.4324.56143.9413.8184.2473.8013.92133.233.1173.5163.1013.20822.4122.3112.6652.2982.38711.4121.3381.6071.3281.3922，t13.1673.1123.2923.1043.1692,t24.7974.7284.9484.724.8011,t11.3491.3411.3621.341.3461,t23.1763.1563.2073.1543.16820.755990.7585530.7571120.7554310.7534531-0.06819-0.06622-0.0678-0.06717-0.06628J0.0237440.0237270.0237230.023790.023873理论值0.02401实际值0.023772误差0.99%4.转动次数（）验证平行轴 80mm 2012.47612.34212.32112.32812.3421911.98211.8511.82911.83511.851811.48911.3611.3411.30311.3591710.99910.87310.85310.85310.8311610.5110.38710.36710.36510.3851510.0249.9049.8849.889.901149.5399.4229.4039.3979.419139.0578.9438.9248.9168.939128.5778.4658.6468.4378.46118.0997.9897.9717.967.985107.6227.5157.4977.4857.5197.1337.0297.0126.9977.02486.6176.5176.56.4836.51276.0715.9755.9585.945.9765.4875.3965.385.3615.39154.8594.7744.7584.7394.76844.1724.0944.084.0594.08833.4093.3383.3253.3043.33222.5332.4722.4622.4392.46511.4721.4261.421.3971.4212，t13.3873.3483.3383.3423.3472,t25.1455.0915.085.0865.0911,t11.4531.4441.4431.4491.4461,t23.4193.3993.3973.4123.40320.6414250.6493740.6475770.6461450.6477161-0.0553-0.05825-0.05901-0.06018-0.05674J0.0280950.0276620.0277020.0277130.027786理论值0.027393实际值0.027792误差1.40%5.转动次数（）验证平行轴 120mm2013.75513.85913.7813.68214.4831913.20713.30913.22913.13113.9251812.66112.76112.67912.58213.3691712.11712.21512.13212.03712.8151611.57611.67111.58711.49212.2641511.03711.13111.04610.95111.7151410.41910.59110.50710.41211.168139.96510.0559.9719.87510.604129.4319.529.4379.3410.082118.9018.9888.9058.8079.542108.3728.4588.3758.2769.00497.837.9137.8317.7338.45287.2577.3397.2587.167.86876.6526.7316.6516.5547.24966.0066.0836.0045.9086.5855.3115.3865.3085.2175.86944.5524.6244.5494.4645.08233.7093.7183.7073.6294.17922.7442.8082.7432.6763.17311.581.6321.581.5321.9022，t13.7313.7543.7283.6853.9672,t25.6775.7075.6785.6285.9661,t11.6111.6161.6161.6171.661,t23.793.8043.8093.8073.87920.5193970.5178150.5148540.5116420.5183491-0.0439-0.04669-0.0535-0.04751-0.00747J0.0347580.0346840.0344490.0350160.037236理论值0.033793实际值0.035229误差4.20%6.转动次数（）验证与外力矩无关 2010.94710.86510.78410.94210.961910.49710.41810.29810.49310.5211810.0489.9729.85310.04510.063179.6029.5299.419.69.617169.1569.0878.9689.1559.172158.7138.6478.5298.7138.73148.2818.2588.0918.2728.259137.8327.2727.6557.8337.85127.3937.3367.227.3967.413116.9576.9036.7886.966.917106.5226.4716.3576.5266.54396.0896.0415.9786.0946.1185.6515.6125.55.6635.67975.2015.1675.0585.2175.23364.7334.694.5844.744.75654.2174.1754.0734.2244.2443.653.613.5133.6583.67333.0162.9792.8883.0243.03822.2792.2462.1662.2872.30111.3661.3411.281.3731.3852，t11.7121.8741.7191.7371.7332,t23