19th Ave New York, NY 95822, USA

# 物理代考|理论力学代考Theoretical mechanics代考|PH314 Theorem of Angular Momentum

my-assignmentexpert™理论力学Theoretical mechanics代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。my-assignmentexpert™， 最高质量的理论力学Theoretical mechanics作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此理论力学Theoretical mechanics作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

my-assignmentexpert™ 为您的留学生涯保驾护航 在物理代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的物理代考服务。我们的专家在理论力学Theoretical mechanics代写方面经验极为丰富，各种理论力学Theoretical mechanics相关的作业也就用不着 说。

## 物理代考|理论力学代考Theoretical mechanics代考|Moment of Inertia of a Rigid Body to an Axis

In comparison with the concept of mass, we here first introduce the concept of moment of inertia (or inertial moment), which depicts the rotation property of the rigid body. As shown in Fig. 12.1, a rigid body is rotating with respect to an axis $z$, with the angular velocity $\omega$. For an arbitrary point $m_{i}$, the length between the particle and the axis $z$ is $r_{i}$, and velocity is $v_{i}$. Clearly, each point on the rigid body is in a circular motion, and the velocity is
$$v_{i}=\omega r_{i} .$$
The moment of inertia about the rigid body to the axis $z$ is defined as
$$J_{z}=\sum m_{i} r_{i}^{2} .$$
Clearly, the moment of inertia is always positive, dependent on the shape, axis and mass distribution of the rigid body. It is not related to the motion state of the rigid body. For a rigid body with continuous distribution of mass, it can be further expressed as
$$J_{z}=\int_{V} r^{2} \mathrm{~d} m=\int_{V} r^{2} \rho \mathrm{d} V,$$
where $V$ is the volume occupied by the rigid body, and $\rho$ is its density of mass.

## 物理代考|理论力学代考Theoretical mechanics代考|Theorem of Angular Momentum

The angular momentum of a particle is defined as
$$\boldsymbol{L}{O}=\boldsymbol{r} \times \boldsymbol{P}=\boldsymbol{r} \times(m v) .$$ Similar to the concept of moment, it can also be decomposed into three components in the three axes, i.e., $$\boldsymbol{L}{O}=L_{x} i+L_{y} j+L_{z} \boldsymbol{k} .$$
The derivative of the angular momentum is
\begin{aligned} \dot{\boldsymbol{L}}{O} &=\dot{\boldsymbol{r}} \times m \boldsymbol{v}+\boldsymbol{r} \times m \dot{\boldsymbol{v}} \ &=\boldsymbol{v} \times m \boldsymbol{v}+\boldsymbol{r} \times m \boldsymbol{a} \ &=\boldsymbol{r} \times \boldsymbol{F} \ &=\boldsymbol{M}{O}(\boldsymbol{F}) . \end{aligned}
Similarly, one has

$$\left{\begin{array}{l} \dot{L}{x}=M{x}(\boldsymbol{F}) \ \dot{L}{y}=M{y}(\boldsymbol{F}) \ \dot{L}{z}=M{z}(\boldsymbol{F}) \end{array}\right.$$
As shown in Fig. 12.4, the angular momentum for a rigid body rotating to an axis $z$ is
$$L_{z}=(\boldsymbol{r} \times m \boldsymbol{v}){z}=\sum r{i} m_{i} v_{i}=\omega \sum m_{i} r_{i}^{2}=J_{z} \omega .$$
For example, as shown in Fig. 12.5, a wheel is rotating with respect to a point $O$. The moment of inertia to point $O$ is
$$J_{O}=\frac{1}{2} m R^{2} .$$
Then the angular momentum of the rigid body to point $O$ is
$$L_{O}=J_{O} \omega=\frac{1}{2} m R^{2} \omega .$$

## 物理代考|理论力学代考THEORETICAL MECHANICS代 考|MOMENT OF INERTIA OF A RIGID BODY TO AN AXIS

$$v_{i}=\omega r_{i}$$

$$J_{z}=\sum m_{i} r_{i}^{2} .$$

$$J_{z}=\int_{V} r^{2} \mathrm{~d} m=\int_{V} r^{2} \rho \mathrm{d} V,$$

## 物理代考|理论力学代考THEORETICAL MECHANICS代 考|THEOREM OF ANGULAR MOMENTUM

$$\boldsymbol{L} O=\boldsymbol{r} \times \boldsymbol{P}=\boldsymbol{r} \times(m v) .$$

$$\boldsymbol{L} O=L_{x} i+L_{y} j+L_{z} \boldsymbol{k} .$$

$$\dot{L} O=\dot{\boldsymbol{r}} \times m \boldsymbol{v}+\boldsymbol{r} \times m \dot{\boldsymbol{v}} \quad=\boldsymbol{v} \times m \boldsymbol{v}+\boldsymbol{r} \times m \boldsymbol{a}=\boldsymbol{r} \times \boldsymbol{F} \quad=M O(\boldsymbol{F}) .$$

$\$ \$$左 1$$
\dot{L} x=M x(\boldsymbol{F}) \dot{L} y=M y(\boldsymbol{F}) \dot{L} z=M z(\boldsymbol{F})
$$正确的。 AsshowninFig. 12.4, theangularmomentum forarigidbodyrotatingtoanaxis \ z \ i s L_{-}{z}=\boldsymbol{r} \times m \boldsymbol{v}{z}=\left{\right. sum r{i} \mathrm{m}{-}{i} v{-}{i}=\backslash o m e g a \mid sum m_{-}{i} r_{-}{i} \wedge{2}=J_{-}{z} \backslash \omega 。 Forexample, asshowninFig. 12.5, awheelisrotatingwithrespecttoapoint \ \$$. Themomentofinertiatopoint \$\$$O is J_{-}{0}=\backslash \operatorname{frac}{1}{2} m \mathrm{R}^{\wedge}{2} Thentheangularmomentumoftherigidbodytopoint \ \ i S L_{-}{0}=J_{-}{O} \backslash lomega= \backslash frac {1}{2} ~ m R^{\wedge}{2} \backslash \omega 。 \ \$$

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。