polar moment of inertia

简明释义

极惯性矩

英英释义

例句

1.To optimize the design, the architect needed to know the polar moment of inertia 极惯性矩 of the materials being used.

为了优化设计，建筑师需要知道所用材料的极惯性矩 polar moment of inertia。

2.In structural analysis, the polar moment of inertia 极惯性矩 is crucial for determining the resistance of beams to twisting.

在结构分析中，极惯性矩 polar moment of inertia 对于确定梁对扭转的抵抗力至关重要。

3.The formula for the polar moment of inertia 极惯性矩 of a solid cylinder is derived from its radius and height.

实心圆柱体的极惯性矩 polar moment of inertia 的公式是由其半径和高度推导而来的。

4.The engineer calculated the polar moment of inertia 极惯性矩 for the circular shaft to ensure it could withstand torsional loads.

工程师计算了圆形轴的极惯性矩 polar moment of inertia，以确保它能够承受扭转载荷。

5.When analyzing the stability of rotating machinery, the polar moment of inertia 极惯性矩 plays a significant role.

在分析旋转机械的稳定性时，极惯性矩 polar moment of inertia 起着重要作用。

作文

The concept of polar moment of inertia is fundamental in the field of engineering and physics, particularly when analyzing the strength and stability of structures. The polar moment of inertia (极惯性矩) is a measure of an object's resistance to torsional deformation, which occurs when a twisting force is applied. Understanding this property is essential for designing components that can withstand rotational forces without failing. In essence, the polar moment of inertia quantifies how mass is distributed relative to an axis of rotation. For instance, consider a cylindrical shaft used in machinery. The distribution of material around its central axis determines how well it can resist twisting. A larger polar moment of inertia indicates that the shaft can endure greater torque before yielding. This is crucial in applications such as automotive and aerospace engineering, where components are subjected to significant torsional loads.To calculate the polar moment of inertia, engineers often use specific formulas depending on the shape of the object. For a solid circular shaft, the formula is J = (π/32) * d^4, where d is the diameter of the shaft. For hollow shafts, the formula changes to J = (π/32) * (d_outer^4 - d_inner^4). These calculations allow engineers to predict how a given design will perform under operational stresses.Moreover, the polar moment of inertia is not just a theoretical concept; it has practical implications in real-world applications. For example, when designing bridges, engineers must consider the polar moment of inertia of various materials to ensure that they can handle the torsional forces caused by wind or traffic loads. Failure to account for this can lead to catastrophic structural failures.In addition to its importance in structural engineering, the polar moment of inertia also plays a vital role in mechanical systems. For rotating machinery, such as turbines and engines, the polar moment of inertia affects the system's angular momentum and energy efficiency. A higher polar moment of inertia means that the system can maintain its rotational speed more effectively, which is critical for performance and longevity.In conclusion, the polar moment of inertia (极惯性矩) is a key property that influences the design and analysis of various engineering structures and mechanical systems. Its ability to quantify resistance to torsion makes it an invaluable tool for engineers seeking to create safe, efficient, and reliable designs. By understanding and applying this concept, engineers can ensure that their structures and machines not only meet but exceed safety standards, ultimately leading to advancements in technology and infrastructure.