刚体的转动惯量
测量刚体的转动惯量
实验目的:
1(用实验方法验证刚体转动定律，并求其转动惯量;
2(观察刚体的转动惯量与质量分布的关系
3(学习作图的曲线改直法，并由作图法处理实验数据。
二.实验原理:
1(刚体的转动定律
具有确定转轴的刚体，在外力矩的作用下，将获得角加速度β，其值与外力矩成正比，与刚体的转动惯量成反比，即有刚体的转动定律:
M = Iβ (1)
利用转动定律，通过实验的方法，可求得难以用计算方法得到的转动惯量。 2(应用转动定律求转动惯量
如图所示，待测刚体由塔轮，伸杆及杆上的配重物组成。刚体将在砝码的拖动下绕竖直轴转动。
设细线不可伸长，砝码受到重力和细线的张力作用，从静止开始以加速度a下落，其运动方
2程为mg – t=ma，在t时间内下落的高度为h=at/2。刚体受到张力的力矩为T和轴摩擦力r力矩M。由转动定律可得到刚体的转动运动方程:T - M = Iβ。绳与塔轮间无相对滑动时frf
有a = rβ，上述四个方程得到:
2m(g - a)r - M = 2hI/rt (2) f
M与张力矩相比可以忽略，砝码质量m比刚体的质量小的多时有a<
表
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达式:
2mgr = 2hI/ rt (3) 式中r、h、t可直接测量到，m是试验中任意选定的。因此可根据(3)用实验的方法求得转动惯量I。
3(验证转动定律，求转动惯量
)出发，考虑用以下两种方法: 从(3
2A(作m – 1/t图法:伸杆上配重物位置不变，即选定一个刚体，取固定力臂r和砝码下落高度h，(3)式变为:
2M = K/ t (4) 1
2式中K = 2hI/ gr为常量。上式表明:所用砝码的质量与下落时间t的平方成反比。实验1
2中选用一系列的砝码质量，可测得一组m与1/t的数据，将其在直角坐标系上作图，应是直线。即若所作的图是直线，便验证了转动定律。
22从m – 1/t图中测得斜率K，并用已知的h、r、g值，由K = 2hI/ gr求得刚体的I。 11
B(作r – 1/t图法:配重物的位置不变，即选定一个刚体，取砝码m和下落高度h为固定值。将式(3)写为:
r = K/ t (5) 2
marquee effect, TV. Video as background, scrolling across the screen, moving. Blinking text and image display effects, such as, secondly, you can use two/three dimensional animation with video added, to effect similar to real people and cartoon characters performing. 4. the programming software the primary function of this software is to make ... System failures, if the problem is caused by improper use of the system, we actively address the required material fee shall be borne by the user. Company system to provide lifelong service, only charge a maintenance fee. 2) company after-sales service personnel regularly visit customers. During the trial operation of the system, we will be left unattended at any time troubleshooting, ensure the normal operation of the system. 3) users when a big event, our company sent technicians to ensure that the smooth settlement of. 4) upgrade service company responsible for the system upgrade, where the company developed the software upgrade for free. 2, and training training points site training, theory training and operation training, variety way, by has rich teaching experience of software engineers is responsible for training, training content including: 1) system General design, and function, and operation, and maintenance 2) corporation dedicated software and the using 3) various equipment of technology conditions, using, maintenance matters, interface and the operation 4) application software, including animation making, and CTV and network of signal interface, and computer, especially strengthened multimedia application, and three dimensional animation making of edit, and Play and Studio operation, play software of operation 5) system software of installation debugging and function expand 6) simple maintenance and fault excluded eighth Department points, and weak system engineering construction organization and the management first section, and construction programme and the construction management a,, and construction programme in determine
1/2式中K = (2hI/ mg)是常量。上式表明r与1/t成正比关系。实验中换用不同的塔轮半径2
r，测得同一质量的砝码下落时间t，用所得一组数据作r,1/t图，应是直线。即若所作图是直线，便验证了转动定律。
1/2从r,1/t图上测得斜率，并用已知的m、h、g值，由K = (2hI/ mg)求出刚体的I. 2
三.实验仪器
刚体转动仪，滑轮，秒表，砝码。
四.实验
内容
财务内部控制制度的内容财务内部控制制度的内容人员招聘与配置的内容项目成本控制的内容消防安全演练内容
1.调节实验装置:调节转轴垂直于水平面
调节滑轮高度，使拉线与塔轮轴垂直，并与滑轮面共面。选定砝码下落起点到地面的高度h，并保持不变。
2.观察刚体质量分布对转动惯量的影响
取塔轮半径为3.00cm，砝码质量为20g，保持高度h不变，将配重物逐次取三种不同的位置，分别测量砝码下落的时间，分析下落时间与转动惯量的关系。本项实验只作定性说明，不作数据计算。
3.测量质量与下落时间关系:
测量的基本内容是:更换不同质量的砝码，测量其下落时间t。
用游标卡尺测量塔轮半径，用钢尺测量高度，砝码质量按已给定数为每个5.0g;用秒表
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下落时间。
将两个配重物放在横杆上固定位置，选用塔轮半径为某一固定值。将拉线平行缠绕在轮上。逐次选用不同质量的砝码，用秒表分别测量砝码从静止状态开始下落到达地面的时间。对每种质量的砝码，测量三次下落时间，取平均值。砝码质量从5g开始，每次增加5g，直到35g止。
用所测数据作图，从图中求出直线的斜率，从而计算转动惯量。
4.测量半径与下落时间关系
测量的基本内容是:对同一质量的砝码，更换不同的塔轮半径，测量不同的下落时间。 将两个配重物选在横杆上固定位置，用固定质量砝码施力，逐次选用不同的塔轮半径，测砝码落地所用时间。对每一塔轮半径，测三次砝码落地之间，取其平均值。注意，在更换半径是要相应的调节滑轮高度，并使绕过滑轮的拉线与塔轮平面共面。由测得的数据作图，从图上求出斜率，并计算转动惯量。
五.实验数据及数据处理:
r-1/t的关系:
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2,3由此关系得到的转动惯量I=1.7810kg ,m，
m-(1/t)2的关系:
,32由此关系得到的转动惯量I= 1.87，10kg,m
六.实验结果:
2,310kg;验证了转动定律并测出了转动惯量。由r-1/t关系得到的转动惯量I=1.78,m，
2,32由m-1/t的关系得到转动惯量I=. 1.87，10kg,m
七.实验注意事项:
1(仔细调节实验装置，保持转轴铅直。使轴尖与轴槽尽量为点接触，使轴转动自如，且不能摇摆，以减少摩擦力矩。
2(拉线要缠绕平行而不重叠，切忌乱绕，以防各匝线之间挤压而增大阻力。
3(把握好启动砝码的动作。计时与启动一致，力求避免计时的误差。
4(砝码质量不宜太大，以使下落的加速度a不致太大，保证a<
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