The Foundations of Physics

菁英小記者_(dá)黃子宸 編輯_劉煜

Physics and its Theories

The study of Physics: physics is a natural science that studies the essence and nature of matter and energy.Since matter and energy are the basic elements that must be involved in all scientific research,physics is one of the most basic disciplines in natural science.From simple problems to complex problems,physics needs to be involved.When people try to understand "why does this thing work this way",physics will be included in the discussion.You may want to ask: how does an airplane fly? Why is the sky blue? Why can an athlete kick a curved ball? Why does the earth revolve around the sun? And so on.The research of physics will go deep into these phenomena and summarize the general laws from them.Physicists find out the patterns by observing and analyzing various phenomena based on matter and energy in nature.These models are called Theories,and common physical theories that can stand the test of experiments are called Laws,until they are proved to be wrong one day.Simply put,classical physics is the process by which people summarize attributes of natural pheromones and find their relationships.When the subject of physics developed sufficiently,that is,in the last century.People began to look for unified measurement standards and methods.In physics,measurement,units and physical quantities are indispensable and must be known before learning physics.

Units and Measurement in Physics

In physical calculation,there are many quantities used to describe the different properties of the world,such as length,temperature and so on.They are all called physical quantities.Measurements of physical quantities are calculated and considered in a scope of units,the SI units are the standardized unit system for the physics nowadays.There are 7 basic units defined by the SI unit system,including:

Second is the SI unit of time,It is equal to the time where Cesium-133 made 9192631770 vibrations(Caused by energy level transition)

Meter is the SI unit of length,It is defined as 1 650 763.73 times the wavelength of the radiation of the transition between 2p10 and 5d1 levels of krypton-86 atom in vacuum.

Dimensional analysis is an important research method in natural science.It analyzes and judges the general law followed by the quantitative relationship between things according to the form that all quantities must have.Through dimensional analysis,we can check whether the equations reflecting the laws of physical phenomena are correct in measurement.(Important in solving either real world or designed physics problems).Dimension may be understood as: what does this physical quantity describe? For example,the unit of meter given just now is used for the calculation and measurement of length,so the dimension of this physical quantity is length.The dimension of any physical quantity indicates its dependence on the basic quantity as the symbolic product.So we know how this physical quantity is derived from the basic physical quantity A equation of any subject must be dimensionally consistent,meaning that the dimension on both side must be equal.For example,we can not compare 35 degrees Celsius with 35 meters,because the dimension of 35 degrees Celsius is the temperature,and 35 meters refers to a length,which is the same regarding the equation.To learn dimensional analysis,it is to learn how to Determine whether an equation involving physical quantities is dimensionally consistent or evaluating the dimension of a mathematical expression.According to the above table,each basic unit has a dimension,which shows that other units can also have dimensions.For example,velocity (average) is the result of displacement divided by time elapsed,and its unit is meters per second.Because displacement is a measure of length,and time in the unit of time,that means the dimension for velocity is:[L][T]-1[L][T]-1;For kinetic energy,given that its is equal to 12mv212mv2,its dimension is [M][L]2[T]-2[M][L]2[T]-2.It can be seen that pure real numbers like half have no dimension.However,in the future,there will be various constants,which may have dimensions and units.

More Examples:

The dimension for Force (F) should be [L][M][T]-2 as it is to that Newton(unit) is equal to Kilogram·Meter per second squared

Question:

Having told that the dimension of momentum is [M][L][T]-1,is the equation p=mv dimensionally consistent? (p represents momentum)

Position

In classical mechanics,the most important part of analyzing the motion of an object is to know the position of the object at a specific time T.because this part only involves one-dimensional motion,then this position can be described only by X.But it is important to choose a reference system first.The reference system is any axis you choose under the system or space where the object is located.The best reference system is the inertial reference system,that is,in this system,this reference system must be inertial or static.For example,when we analyze objects in daily life,we can use the earth as the reference system,and when we analyze the moving point on the X axis,we can use the axis itself.

Displacement

If an object is moving and moving relative to this reference system,then from the beginning time T1 to T2,it must have moved from position X1 to x2.The difference between X1 and X2 is collectively called displacement.For example,John moved from one corner of the house to another,so he moved relative to the house.And it can be found that this displacement has direction and size(length).Then we can treat displacement as a vector.Then,the formula for calculating the displacement is very obvious,that is:

deltax=x1-x0

Moreover,if an object is displaced many times,its final displacement or total displacement is the sum of these displacements.Taking the motion on the one-dimensional X-axis as an example,a ball starts from the origin,moves 2 meters in the positive direction,and then moves 1 meter in the opposite direction.Then the calculation is as follows: 2=X1-0-1=X2-x1,then the final X2 is equal to 1,and the total displacement is 2-1=1.At the same time,1=X2-0,the two formulas are actually equal.

Velocity

At this point,someone must ask,so how can we judge which object moves faster in a certain direction.In fact,we just need to judge who spends less time in the same displacement in this direction.When an object t0 reaches T1 at x0 after a period of time,and the object moves to x1,then its average velocity can be calculated by dividing its displacement by the time it takes.v avg=x1-x0/t1 -t0.The denominator meas the elapsed time delta T and the numerator means the displacement.This formula tells us that if a two object has the same displacement,but takes different time,the shorter the time,the greater the velocity.Because displacement has direction and size,so does velocity.If someone tells us the average velocity and the time spent in motion,we can calculate the displacement of the object.If you tell us the initial position x0 again,we can use the previous displacement formula to calculate the final position of the object x1.Of course,the average velocity has great limitations.We can only know how fast the displacement of this object is probably or on average during this period of time through the average velocity,but we are not sure about the velocity of this object under a specific t.Then,the introduction of a new definition -instantaneous velocity can solve this problem.Instantaneous velocity is to differentiate displacement or to take its derivative with respect to time.Then the instantaneous velocity under a certain T is ds/dt(s is displacement),which is also limit delta T→0 {delta s/delta t}|t,which means that the meaning of instantaneous velocity is the ratio of displacement to 23time lapse at a specific time t (because delta T approaches 0).It can also be written as d/dt (x (T): find the derivative of position or displacement function with respect t time to time.Instantaneous velocity is a more accurate existence than the average velocity,and it allows people to choose any time t and analyze the speed of the object at that moment.Instantaneous velocity is a more accurate existence than the average velocity,and it allows people to choose any time t and analyze the speed of the object at that moment.If the speed does not remain the same in motion,we call it accelerating.For example,if a car needs to move from a stationary state to 60km per hour when starting,the driver needs to accelerate the car through the engine.Acceleration is the rate of change of velocity,that is,the ratio of velocity change to time change.In the same way as the evaluation of velocity,the formula of draw acceleration is: a AVG=V1-V0/T1-T0,the numerator is the change of velocity in this time interval,and the denominator is also the consumption of time.If the speed of an object changes more at the same time,the acceleration it receives is also greater.It is obvious that the instantaneous acceleration is the ratio of the change of the speed of an object moving at this instant to time that we know at any time.That is,a=dv/dt

Motion with Constant Acceleration

we have not developed a specific equation that relates acceleration and displacement.In this section,we look at some convenient equations for kinematic relationships,starting from the definitions of displacement We now make the important assumption that acceleration is constant.This assumption allows us to avoid using calculus to find instantaneous acceleration.Since acceleration is constant,the average and instantaneous accelerations are equal—that is a.since we have the notation that v avg=x1-x0/delta t.Which means x1=x0+v avg ＊ delta t .Another convenient formula that connects a and v is v1=v0+a(constant) delta t.

To derive a convinient way to calculate displacement directly from acceleration,initial speed is this:

V1=v0+a ＊ t

V0+v1=v0+1/2 a ＊ t

As we substitute in x1=x0+v avg t

We get x1=x0+v0t+1/2 a ＊ t^2.

This can also be derived by using calculating the integral of instantaneous velocity,is instantaneous velocity is actually the derivative of displacement,in which the initial condition for this intergral is the initial position.

If we substitude v avg=v1+v0/2 and t=v1-v0/a into x1=x0+v avg t,we get v1^2 -v0^2=2 a delta x.Then we got to solve kinetic problems with out given time,but needed to solve for relationship between displacement and acceleration.The note that follows is provided for easy reference to the equations needed.Be aware that these equations are not independent.In many situations we have two unknowns and need two equations from the set to solve for the unknowns.We need as many equations as there are unknowns to solve a given situation.