Quantity Model

In engineering and scientific calculations, people are often confused because of the dizzying number and units of physics. The reason is that we first consider unit conversion rather than considering the conversion relationship between quantities before calculating. For example, when we calculate the force of an object in motion, Newton's second law should be used. We wrote the formula first\(a=\frac{m\times l}{t^{2}}\). After that, we will examine the formula of each physical quantity(m, l, t), and then do the unit conversion. When there are many such calculationsthe and formula is complicated, you will often get lost here and lose the opportunity to understand the results of the calculations.

The reason is that we pay too much attention to the conversion of units and neglect the relationship between the various physical quantities in the calculation process, and we confuse the unit of measurement, the dimension and the physical nature of the physical quantity itself, so we often Lost in this calculation. Then people will definitely ask a question, that is, what is the nature of physical quantity, what is the dimension, and what is the unit of physical quantity, and so on.

physical quantity

I personally believe that in the physical world, every thing has its attributes. We look for these attributes and their relationships, and we can understand the characteristics of things based on these attributes and their relationships. No matter how we measure these properties, it always exists. For example, when an object rotates, it must have speed, acceleration, and displacement, and it is also related to time. Therefore, when studying the motion of an object, its attributes include displacement, velocity, and acceleration. Of course, time is also one of the key attributes of the motion of an object. These attributes and relationships exist in essence, and their existence has nothing to do with our understanding, and it has nothing to do with how we measure them.

unit of measurement

We can always predict other attributes of certain things in the physical world by measuring certain physical quantities and based on correlations. For example, according to Newton's second law of motion of an object, if we measure its mass and force, we can calculate its acceleration. If no longer based on the relationship between acceleration, displacement and time, we can also predict where the object will arrive in how long.

Therefore, the measurement of physical quantity is a necessary means for science and engineering to understand the world and use the laws of nature. The essence of measurement is comparison. For example, when we measure the length of an object, we always compare the fixed length of another object with the length of the object being measured. In daily life, we use a ruler to measure the length of cloth, that is, the length of the ruler is 1, to see how many rulers the length of the cloth has. The magnitude from compared value is the of the measured physical quantity of cloth length, and its unit is one ruler.

The size of the ruler can be arbitrary, as long as the same ruler is used every time to ensure that the results of each measurement are comparable. The length of a person's elbow has been used as a ruler in history.

Essentially, each type of physical quantity should have its own unit of measurement, and the attributes of these units of measurement are determined by the characteristics of the type of physical quantity. For example, the physical quantity of length type must have the characteristic of length in its unit of measurement, and the unit of measurement of speed cannot be used to measure length. Therefore, each quantity type determines its unit of measurement attributes. But what numberical value can be used as the measurement unit of the physical quantity is arbitrarily chosen by people.

One type of physical quantity requires one type of measurement unit. However, there are many things in our world, and there are more physical quantities that need to be measured. If the unit of measurement is defined for each type of physical quantity, the workload is extremely huge and it is a difficult task to complete. Therefore, people often choose a few from a large number of physical quantities, and define units specifically for them, which are called basic units. The units of other physical quantities are directly derived from these basic units, and the basis for the derivation is the basic relationship between these physical quantities. For example, the unit of measurement for length is meters, and the relationship between area and length is length multiplied by length, so the unit is also meters by meters, that is, square meters. By setting the basic unit, the derived unit is generated from the basic unit, and then a new derived unit is generated from the basic unit and the derived unit, so that the unit of measurement can be conveniently defined for the numerous quantities in the world we are studying.

It is worth noting that what kind of physical quantity is chosen as the basic unit is also a choice made by humans, and it will not change the equal relationship between physical quantities. From the point of view of scientific principles, there is no basic physical quantity and derived physical quantity in physical quantity, so there is no high or low unit of measurement. In the unit system, physical quantities are divided into basic physical quantities and derived physical quantities, and measurement units are divided into basic measurement units and derived measurement units, which are purely determined by humans for the convenience of defining the specific value of the measurement unit. This should not make us mistakenly think that understanding the unit of measurement and the basic unit of measurement is more important than understanding the nature of physical quantities.

In the process of calculating physical quantities, people use some common quantities as the basis. According to the relationship between physical quantities, it is determined that certain quantities can be derived from other quantities. The purpose is also to simplify calculations and select units. Starting from the relationship between the physical world, people found that the two sides of the equal sign of the equation of the laws of nature, the power exponents of their physical quantities should be equal. From here, people also developed a set of dimensional analysis methods to analyze the laws of the physical world. The core is to use several selected dimensions as the basis, and through mathematical transformations, the relationship between quantities can be expressed more simply and clearly. But from the physical essence, dimensions are unnecessary artifacts. Especially in the calculations between physical quantities that have a clear relationship, the dimensions are often confusing. Without going through the dimension, as long as we clearly know what type of physical quantity will be obtained in each step of the calculation, the choice of the unit is also very simple, and it has nothing to do with whether the dimension is used or not.

When the derived unit is used in the SI unit system, because the expression of the unit is related to the basic unit, the dimension corresponding to the basic unit is specified, and its essence is for the convenience of narrative. It has nothing to do with whether dimensions are essentially required in physics. Below we will discuss the SI unit system.

In the SI unit system, most units are derived from a few units. Due to the complexity of the physical world and the complexity of calculations, it is inevitable that many units of physical quantities will be the same. For example, the units of energy, work and heat are the same, and the units of heat capacity and entropy, specific heat capacity and specific heat entropy are also the same. Therefore, although each physical quantity has its own unit, a certain unit does not only correspond to one physical quantity. When calculating, it is not advisable to calculate the unit of the result physical quantity first, and then determine the type of the physical quantity. In addition, the unit of energy is N·m, and the unit of torque is also N·m, but they are two completely different types of physical quantities, which are the same as parameters, work and heat units, but are different from heat capacity and entropy. There are similarities and differences between specific heat capacity and specific heat entropy. These domain characteristics require us to be very careful when programming calculations.

SI unit System

Although the size of the unit can be chosen arbitrarily, it is also possible to choose any thing as the unit of measurement. However, in order to ensure the stability of the measurement unit, people continue to improve this choice, making the reproducibility of the measurement unit more and more guaranteed. In the long-term process, people have gradually determined a set of choices and formed various levels of measurement standards to ensure the stability and comparability of people's measurement results in scientific research, engineering practice, and daily life. The SI unit system is one of these unit systems.

The SI unit system first stipulates that seven physical quantities are their basic quantities, and their units are basic units. Then, according to the principle of simplicity, use the relationship between physical quantities to derive the units of other physical quantities, which is part of the derived units. Using the basic unit and these derived units, and further deriving other physical quantity units, you can define as many physical quantity units as possible.

An outstanding feature of the SI unit system is that all units have a coherent unit, and this unit is selected for calculation, so that when people use the laws of physics to calculate, no additional unit conversion coefficients will be added to the physics formula. For example, when choosing the meter, second, kg in the SI unit value as the unit, and using Newton’s second law to calculate the force on an object, its formula is \(F=ma=m\times l/t^{2}\), There are no coefficients due to unit conversion. This brings a lot of cheapness to our calculations. Before calculating, we can convert the unit of measurement of each physical quantity to coherent unit in advance. The measurement unit of the final result is also the coherent unit of the calculated physical quantity. Using this method to calculate physical quantities allows us to pay more attention to the nature of calculations and the physical meaning of calculations in the calculation process, without getting lost in dazzling measurement units.

The Physical Quantity Calculating class library

In physical quantity calculating class library, the unit of measurement that can be processed is the SI measurement unit, including the non-SI measurement unit used by SI. It also provides a conversion interface between other commonly used units and SI measurement units. More importantly, the use of the physical quantity calculation class library can force us to clearly know the type of the result quantity of each step in the process of programming calculation, and select the corresponding measurement unit on this basis to ensure that the type of the calculation result is the accuracy of the unit.