dimensional formula

简明释义

因次公式

英英释义

例句

1.Understanding the dimensional formula 维度公式 helps in dimensional analysis and conversion.

理解维度公式 维度公式 有助于维度分析和转换。

2.When calculating energy, you can use the dimensional formula 维度公式 [M L^2 T^-2].

在计算能量时，可以使用维度公式 维度公式 [M L^2 T^-2]。

3.The dimensional formula 维度公式 for pressure is derived from force per unit area.

压力的维度公式 维度公式 是从单位面积上的力推导而来的。

4.In physics, the dimensional formula 维度公式 of force is expressed as [M L T^-2].

在物理学中，力的维度公式 维度公式 表示为 [M L T^-2]。

5.The dimensional formula 维度公式 for velocity is [L T^-1], indicating how distance changes over time.

速度的维度公式 维度公式 是 [L T^-1]，表示距离随时间的变化。

作文

In the field of physics and engineering, understanding the concept of a dimensional formula is crucial for analyzing various physical quantities. A dimensional formula is a mathematical expression that represents the dimensions of a physical quantity in terms of fundamental dimensions such as mass, length, time, electric current, temperature, amount of substance, and luminous intensity. These fundamental dimensions are often denoted by symbols: M for mass, L for length, T for time, I for electric current, θ for temperature, N for amount of substance, and J for luminous intensity.For example, consider the physical quantity of velocity. Velocity is defined as the rate of change of displacement with respect to time. The dimensional formula for velocity can be derived from its definition. Displacement has the dimension of length (L), and time has the dimension of time (T). Therefore, the dimensional formula for velocity is represented as [L][T]⁻¹, indicating that velocity has one dimension of length and an inverse dimension of time.Another important example is that of force. According to Newton's second law of motion, force is defined as the mass of an object multiplied by its acceleration. The dimensional formula for mass is [M], while acceleration is the rate of change of velocity with respect to time. Since velocity has the dimensional formula of [L][T]⁻¹, acceleration, which is the change in velocity per unit time, has the dimensional formula of [L][T]⁻². Thus, the dimensional formula for force becomes [M][L][T]⁻².Understanding dimensional formulas is not only essential for calculations but also serves as a powerful tool for checking the consistency of equations in physics. When deriving formulas, scientists can use dimensional analysis to ensure that both sides of an equation have the same dimensional formula. If they do not match, it indicates an error in the derivation or in the assumptions made during the process.Additionally, dimensional formulas can help in converting units from one system to another. For instance, if we want to convert a measurement from meters per second to kilometers per hour, we can utilize the dimensional formula for velocity to guide our conversion process. By understanding the dimensions involved, we can systematically approach the conversion without making mistakes.In conclusion, the concept of a dimensional formula is fundamental in the study of physics and engineering. It provides a clear representation of the dimensions of physical quantities, aids in dimensional analysis for ensuring equation consistency, and assists in unit conversions. Mastering the use of dimensional formulas enhances one’s ability to solve complex problems and deepens the understanding of the relationships between different physical quantities. As students and professionals in these fields continue to explore the intricacies of the universe, the importance of dimensional formulas will undoubtedly remain a cornerstone of scientific inquiry and application.

在物理和工程领域，理解“dimensional formula”的概念对于分析各种物理量至关重要。“dimensional formula”是一个数学表达式，表示物理量相对于基本维度（如质量、长度、时间、电流、温度、物质的量和光强度）的维度。这些基本维度通常用符号表示：质量用M表示，长度用L表示，时间用T表示，电流用I表示，温度用θ表示，物质的量用N表示，光强度用J表示。例如，考虑速度这一物理量。速度被定义为位移随时间变化的速率。速度的“dimensional formula”可以从其定义中推导出来。位移的维度为长度（L），而时间的维度为时间（T）。因此，速度的“dimensional formula”表示为[L][T]⁻¹，表明速度具有一个长度维度和一个时间的倒数维度。另一个重要的例子是力。根据牛顿第二运动定律，力被定义为物体的质量乘以其加速度。质量的“dimensional formula”为[M]，而加速度是速度随时间变化的速率。由于速度的“dimensional formula”为[L][T]⁻¹，因此加速度，即单位时间内速度的变化，其“dimensional formula”为[L][T]⁻²。因此，力的“dimensional formula”变为[M][L][T]⁻²。理解“dimensional formulas”不仅对计算至关重要，而且作为检查物理方程一致性的有力工具。当推导公式时，科学家可以使用维度分析来确保方程的两边具有相同的“dimensional formula”。如果它们不匹配，则表明推导或过程中所做的假设存在错误。此外，“dimensional formulas”还可以帮助将单位从一个系统转换到另一个系统。例如，如果我们想将测量值从米每秒转换为公里每小时，我们可以利用速度的“dimensional formula”来指导我们的转换过程。通过理解所涉及的维度，我们可以系统地进行转换而不出错。总之，“dimensional formula”的概念在物理和工程研究中是基础。它提供了物理量维度的清晰表示，帮助进行维度分析以确保方程的一致性，并协助单位转换。掌握“dimensional formulas”的使用增强了人们解决复杂问题的能力，加深了对不同物理量之间关系的理解。随着学生和专业人士继续探索宇宙的复杂性，“dimensional formulas”的重要性无疑将继续成为科学探究和应用的基石。