moment of inertia

简明释义

惯性矩

英英释义

例句

1.When analyzing a beam, engineers must calculate its moment of inertia 惯性矩 to determine its strength.

在分析梁时，工程师必须计算其惯性矩 moment of inertia 以确定其强度。

2.The moment of inertia 惯性矩 of a solid cylinder is calculated using the formula I = (1/2) * m * r^2.

一个实心圆柱体的惯性矩 moment of inertia 是通过公式 I = (1/2) * m * r^2 计算的。

3.In engineering, understanding the moment of inertia 惯性矩 helps in designing safer structures.

在工程学中，理解惯性矩 moment of inertia 有助于设计更安全的结构。

4.A higher moment of inertia 惯性矩 means that more torque is required to achieve the same angular acceleration.

更高的惯性矩 moment of inertia 意味着需要更多的扭矩来实现相同的角加速度。

5.The moment of inertia 惯性矩 affects how easily an object can be rotated around an axis.

物体绕某一轴旋转的难易程度受惯性矩 moment of inertia 的影响。

作文

The concept of moment of inertia is fundamental in the field of physics and engineering, particularly when dealing with rotational motion. It can be defined as a measure of an object's resistance to changes in its rotation about a particular axis. The moment of inertia depends not only on the mass of the object but also on how that mass is distributed relative to the axis of rotation. This is why two objects with the same mass can have different moments of inertia if their mass distributions are different.To illustrate this, consider a solid disk and a hollow cylinder, both with the same mass and radius. When they are spun around their central axes, the solid disk will have a smaller moment of inertia compared to the hollow cylinder. This means that it will accelerate more quickly when a torque is applied. The mathematical expression for moment of inertia is given by the integral of the mass distribution: I = ∫ r² dm, where 'I' is the moment of inertia, 'r' is the distance from the axis of rotation, and 'dm' is the mass element.Understanding the moment of inertia is crucial in various applications. For instance, in mechanical engineering, it plays a vital role in the design of rotating machinery, such as flywheels and gears. Engineers must calculate the moment of inertia to ensure that these components can withstand the forces acting upon them during operation. A miscalculation could lead to catastrophic failures, making the understanding of this concept essential for safety and efficiency.In addition to engineering, the moment of inertia is also significant in sports and biomechanics. Athletes often optimize their performance by adjusting their body position to alter their moment of inertia. For example, a figure skater pulls in their arms during a spin to decrease their moment of inertia, allowing them to spin faster. This principle illustrates how the moment of inertia is not just a theoretical concept but has real-world implications in enhancing human performance.Moreover, the moment of inertia is also relevant in astrophysics. Celestial bodies, such as planets and stars, rotate around their axes, and their moments of inertia influence their rotational dynamics. Understanding how mass is distributed within these bodies helps scientists explain phenomena such as the stability of planetary orbits and the formation of galaxies.In conclusion, the moment of inertia is a critical concept that transcends multiple disciplines, including physics, engineering, sports, and astrophysics. Its importance lies in its ability to describe how objects behave when subjected to rotational forces. By grasping the principles behind the moment of inertia, one can gain deeper insights into the mechanics of motion and the underlying laws governing our universe. Whether in designing safe machinery, optimizing athletic performance, or studying celestial phenomena, the moment of inertia remains a key factor that cannot be overlooked.

转动惯量的概念在物理学和工程学领域中是基础性的，特别是在处理旋转运动时。它可以定义为物体抵抗其绕特定轴旋转变化的能力的度量。转动惯量不仅取决于物体的质量，还取决于该质量相对于旋转轴的分布方式。这就是为什么两个质量相同的物体，如果它们的质量分布不同，可能会具有不同的转动惯量。为了说明这一点，考虑一个实心圆盘和一个空心圆柱体，它们的质量和半径相同。当它们围绕中心轴旋转时，实心圆盘的转动惯量将比空心圆柱体小。这意味着在施加扭矩时，实心圆盘的加速会更快。转动惯量的数学表达式由质量分布的积分给出：I = ∫ r² dm，其中'I'是转动惯量，'r'是距离旋转轴的距离，'dm'是质量元素。理解转动惯量在各种应用中至关重要。例如，在机械工程中，它在旋转机械的设计中发挥着重要作用，如飞轮和齿轮。工程师必须计算转动惯量，以确保这些组件能够承受操作过程中施加的力量。错误的计算可能导致灾难性的故障，因此理解这一概念对安全性和效率至关重要。除了工程学，转动惯量在体育和生物力学中也很重要。运动员通过调整身体姿势来优化表现，从而改变他们的转动惯量。例如，花样滑冰选手在旋转时收拢手臂以减少转动惯量，使他们能够更快地旋转。这个原理说明了转动惯量不仅是一个理论概念，而且在提高人类表现方面具有现实意义。此外，转动惯量在天体物理学中也与之相关。天体，如行星和恒星，绕其轴旋转，其转动惯量影响其旋转动力学。理解这些天体内部质量的分布有助于科学家解释诸如行星轨道的稳定性和星系的形成等现象。总之，转动惯量是一个关键概念，跨越多个学科，包括物理学、工程学、体育和天体物理学。它的重要性在于它能够描述物体在受到旋转力时的行为。通过掌握转动惯量背后的原理，人们可以深入了解运动的机制及支配我们宇宙的基本法则。无论是在设计安全的机械、优化运动表现，还是研究天体现象，转动惯量始终是一个不可忽视的关键因素。