moment of inertia

简明释义

惯性力矩；转动惯量

英英释义

例句

1.The moment of inertia is crucial in determining how a rotating object behaves under applied forces.

在确定旋转物体在施加力下的行为时，惯性矩至关重要。

2.In physics, the moment of inertia can be calculated using the mass distribution of an object.

在物理学中，惯性矩可以通过物体的质量分布来计算。

3.To reduce vibrations, the moment of inertia of the rotor was increased.

为了减少振动，转子的惯性矩被增加了。

4.Engineers must calculate the moment of inertia of beams to ensure structural stability.

工程师必须计算梁的惯性矩以确保结构的稳定性。

5.The moment of inertia of a cylinder is different from that of a sphere.

圆柱体的惯性矩与球体的不同。

作文

The concept of moment of inertia is fundamental in the study of physics and engineering. It refers to the quantity that determines the torque needed for a desired angular acceleration about a rotational axis. In simpler terms, the moment of inertia (转动惯量) measures how difficult it is to change the rotational motion of an object. The greater the moment of inertia, the more torque is required to accelerate the object. To understand this concept better, let us consider everyday examples. Take a figure skater performing a spin. When the skater pulls their arms close to their body, they reduce their moment of inertia. As a result, they spin faster. Conversely, when they extend their arms outward, their moment of inertia increases, causing them to spin more slowly. This phenomenon illustrates how the distribution of mass relative to the axis of rotation affects the moment of inertia.Mathematically, the moment of inertia can be expressed as the sum of the products of each mass element and the square of its distance from the axis of rotation. For a rigid body, this can be represented by the formula: I = Σ(m_i * r_i²), where I is the moment of inertia, m_i is the mass of each particle, and r_i is the distance from the axis of rotation. Different shapes have different formulas to calculate their moment of inertia. For instance, a solid cylinder has a moment of inertia given by I = 1/2 * m * r², where m is the mass and r is the radius of the cylinder.Understanding the moment of inertia is crucial in various applications. In mechanical engineering, it plays a significant role in the design of rotating machinery, such as flywheels and gears. Engineers must account for the moment of inertia to ensure that these machines operate efficiently and safely. For example, in the automotive industry, understanding the moment of inertia helps in designing vehicles that can handle turns without tipping over.In addition to engineering, the moment of inertia is also essential in sports science. Coaches and athletes study the moment of inertia to improve performance in activities like gymnastics, diving, and swimming. By manipulating their body positions, athletes can optimize their moment of inertia to enhance their speed and control during performances.Moreover, the moment of inertia is not only limited to rigid bodies. In the field of astrophysics, celestial bodies such as planets and stars also exhibit a moment of inertia. Understanding the moment of inertia of these celestial objects helps scientists comprehend their rotational dynamics and stability.In conclusion, the moment of inertia is a vital concept that influences various fields, from engineering to sports science and astrophysics. Its understanding allows us to predict how objects will behave when subjected to rotational forces. Whether you are a student learning about physics or an engineer designing complex machinery, grasping the significance of the moment of inertia is essential for success. As we continue to explore the laws of motion, the moment of inertia remains a cornerstone of our understanding of rotational dynamics.

转动惯量的概念在物理学和工程学的研究中是基础性的。它指的是确定所需角加速度所需扭矩的量。简单来说，转动惯量衡量了改变物体旋转运动的难易程度。转动惯量越大，所需的扭矩就越大。为了更好地理解这个概念，让我们考虑一些日常例子。以花样滑冰运动员旋转为例。当运动员将手臂靠近身体时，他们会减少自己的转动惯量。因此，他们旋转得更快。相反，当他们将手臂伸展到外面时，他们的转动惯量增加，导致旋转速度减慢。这个现象说明了质量相对于旋转轴的分布如何影响转动惯量。从数学上讲，转动惯量可以表示为每个质量元素与其距旋转轴的距离的平方的乘积之和。对于一个刚体，这可以用公式表示：I = Σ(m_i * r_i²)，其中I是转动惯量，m_i是每个粒子的质量，r_i是离旋转轴的距离。不同形状的物体计算其转动惯量的公式各不相同。例如，一个固体圆柱体的转动惯量由I = 1/2 * m * r²给出，其中m是质量，r是圆柱体的半径。理解转动惯量在各种应用中至关重要。在机械工程中，它在旋转机械的设计中起着重要作用，例如飞轮和齿轮。工程师必须考虑转动惯量，以确保这些机器高效、安全地运行。例如，在汽车工业中，理解转动惯量有助于设计能够在转弯时不翻倒的车辆。除了工程学，转动惯量在体育科学中也同样重要。教练和运动员研究转动惯量以提高体操、跳水和游泳等活动的表现。通过操控身体姿势，运动员可以优化他们的转动惯量，以增强在表演中的速度和控制力。此外，转动惯量不仅限于刚体。在天体物理学领域，像行星和恒星这样的天体也表现出转动惯量。理解这些天体的转动惯量有助于科学家理解它们的旋转动力学和稳定性。总之，转动惯量是一个影响多个领域的重要概念，从工程学到体育科学和天体物理学。它的理解使我们能够预测物体在受到旋转力时的行为。无论你是学习物理的学生，还是设计复杂机械的工程师，掌握转动惯量的重要性对成功至关重要。随着我们继续探索运动规律，转动惯量仍然是我们理解旋转动力学的基石。