dimensional formula

简明释义

量纲公式

英英释义

例句

1.To derive the dimensional formula of energy, one must consider work done against a force.

要推导出 能量的维度公式，必须考虑对抗力所做的功。

2.In engineering, knowing the dimensional formula helps in dimensional analysis and unit conversions.

在工程中，了解 维度公式 有助于维度分析和单位转换。

3.The dimensional formula for pressure is [M1 L-1 T-2], indicating mass per unit area.

压力的维度公式 是 [M1 L-1 T-2]，表示单位面积上的质量。

4.The dimensional formula for force is represented as [M1 L1 T-2].

力的维度公式 表示为 [M1 L1 T-2]。

5.In physics, the dimensional formula is used to express the physical dimensions of a quantity.

在物理学中，维度公式 用于表达一个量的物理维度。

作文

The concept of the dimensional formula plays a crucial role in the field of physics and engineering. It is a way to express physical quantities in terms of basic dimensions such as mass, length, time, temperature, electric current, amount of substance, and luminous intensity. By using a dimensional formula, we can understand how different physical quantities relate to one another and how they can be transformed or converted. For instance, consider the quantity of velocity. Velocity is defined as the rate of change of displacement with respect to time. Its dimensional formula can be expressed as [L T^-1], where [L] represents length and [T] represents time. This notation indicates that velocity has dimensions of length per unit time. Understanding this dimensional formula helps us analyze problems in mechanics more effectively. Similarly, the dimensional formula for force is derived from Newton's second law of motion, which states that force equals mass times acceleration. The dimensional formula for mass is [M], and acceleration has the dimensional formula of [L T^-2]. Therefore, the dimensional formula for force can be expressed as [M L T^-2]. This relationship not only aids in calculations but also provides insights into the nature of force itself. In addition to aiding calculations, dimensional formulas are essential for checking the consistency of equations in physics. When deriving new equations, scientists often use dimensional analysis to ensure that both sides of an equation have the same dimensional formula. For example, if we derive an equation for energy, we find that it should have the same dimensional formula as work, which is [M L^2 T^-2]. If our derived equation does not match this dimensional formula, we know there is an error in our derivation. Moreover, dimensional formulas can also help in converting units. For example, if we want to convert speed from kilometers per hour to meters per second, understanding the dimensional formula of speed allows us to set up the conversion correctly. We know that 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds. Thus, using the dimensional formula as a guide, we can perform the conversion systematically. The importance of dimensional formulas extends beyond theoretical applications; they are also practical tools in engineering and technology. Engineers frequently rely on dimensional formulas when designing structures or systems to ensure that all components will function together correctly. By understanding the dimensional formula of the materials and forces involved, engineers can predict how structures will behave under various conditions. In conclusion, the dimensional formula is a fundamental aspect of understanding physical quantities and their relationships. It serves as a powerful tool for analysis, ensuring consistency in equations, aiding in unit conversions, and guiding practical applications in engineering. As students and professionals in the sciences continue to explore the complexities of the physical world, mastering the concept of the dimensional formula will undoubtedly enhance their ability to solve real-world problems effectively.

“维度公式”的概念在物理和工程领域中发挥着至关重要的作用。它是一种以质量、长度、时间、温度、电流、物质的量和光强等基本维度来表达物理量的方式。通过使用“维度公式”，我们可以理解不同物理量之间的关系以及它们如何被转换或转化。例如，考虑速度这一量。速度被定义为位移随时间变化的速率。它的“维度公式”可以表示为[L T^-1]，其中[L]代表长度，[T]代表时间。这种符号表示速度的维度是每单位时间的长度。理解这个“维度公式”有助于我们更有效地分析力学问题。同样，力的“维度公式”是从牛顿第二运动定律得出的，该定律表明力等于质量乘以加速度。质量的“维度公式”为[M]，而加速度的“维度公式”为[L T^-2]。因此，力的“维度公式”可以表示为[M L T^-2]。这种关系不仅有助于计算，还提供了对力本质的深入理解。除了帮助计算外，“维度公式”对于检查物理方程的一致性也是必不可少的。在推导新方程时，科学家们常常利用维度分析来确保方程的两侧具有相同的“维度公式”。例如，如果我们推导出一个能量的方程，我们发现它应该与功的“维度公式”相同，即[M L^2 T^-2]。如果我们推导出的方程与这个“维度公式”不符，我们就知道我们的推导存在错误。此外，“维度公式”还可以帮助单位转换。例如，如果我们想将速度从千米每小时转换为米每秒，理解速度的“维度公式”使我们能够正确设置转换。我们知道1千米等于1000米，1小时等于3600秒。因此，利用“维度公式”作为指导，我们可以系统地进行转换。“维度公式”的重要性不仅限于理论应用；它们还是工程和技术中的实际工具。工程师在设计结构或系统时经常依赖“维度公式”，以确保所有组件能够正确协同工作。通过理解材料和力量的“维度公式”，工程师可以预测结构在各种条件下的行为。总之，“维度公式”是理解物理量及其关系的基本方面。它作为分析的强大工具，确保方程的一致性，帮助单位转换，并指导工程中的实际应用。随着科学领域的学生和专业人士继续探索物理世界的复杂性，掌握“维度公式”的概念无疑将增强他们有效解决现实问题的能力。