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所在平台: Udemy |
课程主页: https://www.udemy.com/course/basic-idea-of-circular-motion-and-rigid-body-rotation/
课程评论：没有评论
### Coursera 课程摘要：圆周运动与刚体转动基础 本课程深入浅出地介绍了圆周运动和刚体转动的基本概念。 **核心内容包括：** * **点粒子圆周运动：** * 解释了圆周运动是一种二维加速运动，始终受到指向圆心、径向向内的向心力的作用。 * 区分了**匀速圆周运动**（仅速度方向改变，由向心力引起）和**非匀速圆周运动**（速度大小和方向均改变，由向心力和切向力共同引起）。 * 强调了**转动惯量**在描述旋转粒子惯性中的重要性。 * **刚体绕轴转动：** * 将刚体转动视为大量相互束缚的点粒子绕同一轴以相同角速度进行的圆周运动的叠加。 * 揭示了刚体转动中**转动惯量**并非标量，而是一个**二阶张量**，可以用一个 3x3 的矩阵表示。 * 介绍了该矩阵的 9 个元素，包括绕三个主轴的惯性矩（3 个）和惯性积（6 个）。当绕主轴转动时，惯性积为零。 * **滚动物体运动：** * 将滚动物体的运动分解为**转动**和**平动**的组合。 * 阐述了在这种组合运动中，总能量是这两种运动能量的总和。 本课程为理解更复杂的旋转力学现象奠定了坚实的基础。
Point particle circular motion is a two dimensional accelerated motion which occurs always under influence of centripetal force when applied on the rotating particle in radially inward sense at every moment of rotation of the particle. This circular motion may be of two types which are uniform circular motion and non uniform circular motion. Uniform circular motion occurs only under influence of centripetal force in which only direction of instantaneous velocity will change but for non uniform circular motion, two forces will be effective which are centripetal force and tangential force and for this kind of circular motion both magnitude and direction of the instantaneous velocity of the rotating particle will change. The most effective parameter for rotating particle in circular motion is moment of inertia which basically gives the rotational inertia of that particle. On the other hand if we consider the rigid body rotation about an axis of rotation then since a rigid body is a collection of a number of highly bound point particles, such rigid body rotation can be considered as the summation of a number of point particles circular motion about the same axis with the same angular speed. If we properly study such rigid body rotation and find the relation among the components of angular momentum with the component of angular speed then we can establish that the moment of inertia for rigid body rotation is not a scalar but it is a tensor of rank 2 which can be expressed by a 3x3 square matrix with 9 elements. Out of these 9 elements, 3 are the normal moment of inertia about the three conventional axes X, Y and Z axes and the remaining 6 elements are 6 product of inertias and these are zero for rotation about principal axes. If we consider the rolling of a circular body over the surface then that motion can be taken as the combination of rotational and translational motion and in that case the total energy of the whole combined motion can be expressed as the sum of energies of that two types of motion.
