So, as they say, from elementary to complex. Let's start with kinetic formulas:
Also, let's remember the movement in a circle:
Slowly but surely, we moved on to a more complex topic - dynamics:
After the dynamics, you can go to statics, that is, to the conditions for the equilibrium of bodies relative to the axis of rotation:
After statics, hydrostatics can also be considered:
Where without the topic “Work, energy and power”. It is on it that many interesting, but difficult tasks are given. Therefore, formulas are indispensable here:
Basic formulas of thermodynamics and molecular physics
The last topic in mechanics is “Vibrations and Waves”:
Now we can safely move on to molecular physics:
Basic formulas of electricity
For many students, the topic of electricity is more difficult than thermodynamics, but it is no less important. So, let's start with electrostatics:
We turn to direct electric current:
Electromagnetic induction is also an important topic for the knowledge and understanding of physics. Of course, formulas on this topic are necessary:
And, of course, where without electromagnetic oscillations:
Basic formulas of optical physics
Let's move on to the next section in physics - optics. Here are 8 basic formulas that you need to know. Rest assured, tasks in optics are a frequent occurrence:
Basic formulas of the elements of the theory of relativity
And the last thing you need to know before the exam. Tasks on this topic come across less frequently than the previous ones, but there are:
Basic formulas of light quanta
These formulas often have to be used due to the fact that a lot of problems come across on the topic “Light quanta”. So let's look at them:
You can end there. Of course, there are still a huge number of formulas in physics, but you don’t need them so much.
These were the basic formulas of physics
In the article, we have prepared 50 formulas that will be needed on the exam in 99 cases out of 100.
Advice: print out all the formulas and take them with you. While typing, you will look at the formulas one way or another, memorizing them. In addition, with the basic formulas in physics in your pocket, you will feel much more confident in the exam than without them.
We hope you enjoy our collection of formulas!
P.S. Did 50 physics formulas suffice for you, or does the article need to be supplemented? Write in the comments.
More than 50 basic physics formulas with explanation updated: November 22, 2019 by: Scientific Articles.Ru
Cheat sheet with formulas in physics for the exam
and not only (may need 7, 8, 9, 10 and 11 classes).
For starters, a picture that can be printed in a compact form.
Mechanics
- Pressure P=F/S
- Density ρ=m/V
- Pressure at the depth of the liquid P=ρ∙g∙h
- Gravity Ft=mg
- 5. Archimedean force Fa=ρ w ∙g∙Vt
- Equation of motion for uniformly accelerated motion
X=X0 + υ 0∙t+(a∙t 2)/2 S=( υ 2 -υ 0 2) /2а S=( υ +υ 0) ∙t /2
- Velocity equation for uniformly accelerated motion υ =υ 0 +a∙t
- Acceleration a=( υ -υ 0)/t
- Circular speed υ =2πR/T
- Centripetal acceleration a= υ 2/R
- Relationship between period and frequency ν=1/T=ω/2π
- Newton's II law F=ma
- Hooke's law Fy=-kx
- Law of universal gravitation F=G∙M∙m/R 2
- The weight of a body moving with acceleration a P \u003d m (g + a)
- The weight of a body moving with acceleration a ↓ P \u003d m (g-a)
- Friction force Ffr=µN
- Body momentum p=m υ
- Force impulse Ft=∆p
- Moment M=F∙ℓ
- Potential energy of a body raised above the ground Ep=mgh
- Potential energy of elastically deformed body Ep=kx 2 /2
- Kinetic energy of the body Ek=m υ 2 /2
- Work A=F∙S∙cosα
- Power N=A/t=F∙ υ
- Efficiency η=Ap/Az
- Oscillation period of the mathematical pendulum T=2π√ℓ/g
- Oscillation period of a spring pendulum T=2 π √m/k
- The equation of harmonic oscillations Х=Хmax∙cos ωt
- Relationship of the wavelength, its speed and period λ= υ T
Molecular physics and thermodynamics
- Amount of substance ν=N/ Na
- Molar mass M=m/ν
- Wed. kin. energy of monatomic gas molecules Ek=3/2∙kT
- Basic equation of MKT P=nkT=1/3nm 0 υ 2
- Gay-Lussac law (isobaric process) V/T =const
- Charles' law (isochoric process) P/T =const
- Relative humidity φ=P/P 0 ∙100%
- Int. ideal energy. monatomic gas U=3/2∙M/µ∙RT
- Gas work A=P∙ΔV
- Boyle's law - Mariotte (isothermal process) PV=const
- The amount of heat during heating Q \u003d Cm (T 2 -T 1)
- The amount of heat during melting Q=λm
- The amount of heat during vaporization Q=Lm
- The amount of heat during fuel combustion Q=qm
- The equation of state for an ideal gas is PV=m/M∙RT
- First law of thermodynamics ΔU=A+Q
- Efficiency of heat engines η= (Q 1 - Q 2) / Q 1
- Ideal efficiency. engines (Carnot cycle) η \u003d (T 1 - T 2) / T 1
Electrostatics and electrodynamics - formulas in physics
- Coulomb's law F=k∙q 1 ∙q 2 /R 2
- Electric field strength E=F/q
- Email tension. field of a point charge E=k∙q/R 2
- Surface charge density σ = q/S
- Email tension. fields of the infinite plane E=2πkσ
- Dielectric constant ε=E 0 /E
- Potential energy of interaction. charges W= k∙q 1 q 2 /R
- Potential φ=W/q
- Point charge potential φ=k∙q/R
- Voltage U=A/q
- For a uniform electric field U=E∙d
- Electric capacity C=q/U
- Capacitance of a flat capacitor C=S∙ ε ∙ε 0/d
- Energy of a charged capacitor W=qU/2=q²/2С=CU²/2
- Current I=q/t
- Conductor resistance R=ρ∙ℓ/S
- Ohm's law for the circuit section I=U/R
- The laws of the last compounds I 1 \u003d I 2 \u003d I, U 1 + U 2 \u003d U, R 1 + R 2 \u003d R
- Parallel laws. conn. U 1 \u003d U 2 \u003d U, I 1 + I 2 \u003d I, 1 / R 1 + 1 / R 2 \u003d 1 / R
- Electric current power P=I∙U
- Joule-Lenz law Q=I 2 Rt
- Ohm's law for a complete chain I=ε/(R+r)
- Short circuit current (R=0) I=ε/r
- Magnetic induction vector B=Fmax/ℓ∙I
- Ampere Force Fa=IBℓsin α
- Lorentz force Fл=Bqυsin α
- Magnetic flux Ф=BSсos α Ф=LI
- Law of electromagnetic induction Ei=ΔФ/Δt
- EMF of induction in moving conductor Ei=Вℓ υ sinα
- EMF of self-induction Esi=-L∙ΔI/Δt
- The energy of the magnetic field of the coil Wm \u003d LI 2 / 2
- Oscillation period count. contour T=2π ∙√LC
- Inductive reactance X L =ωL=2πLν
- Capacitance Xc=1/ωC
- The current value of the current Id \u003d Imax / √2,
- RMS voltage Ud=Umax/√2
- Impedance Z=√(Xc-X L) 2 +R 2
Optics
- The law of refraction of light n 21 \u003d n 2 / n 1 \u003d υ 1 / υ 2
- Refractive index n 21 =sin α/sin γ
- Thin lens formula 1/F=1/d + 1/f
- Optical power of the lens D=1/F
- max interference: Δd=kλ,
- min interference: Δd=(2k+1)λ/2
- Differential grating d∙sin φ=k λ
The quantum physics
- Einstein's formula for the photoelectric effect hν=Aout+Ek, Ek=U ze
- Red border of the photoelectric effect ν to = Aout/h
- Photon momentum P=mc=h/ λ=E/s
Physics of the atomic nucleus
The session is approaching, and it's time for us to move from theory to practice. Over the weekend, we sat down and thought that many students would do well to have a collection of basic physics formulas handy. Dry formulas with explanation: short, concise, nothing more. A very useful thing when solving problems, you know. Yes, and at the exam, when exactly what was cruelly memorized the day before can “jump out” of my head, such a selection will serve you well.
Most of the tasks are usually given in the three most popular sections of physics. This Mechanics, thermodynamics And Molecular physics, electricity. Let's take them!
Basic formulas in physics dynamics, kinematics, statics
Let's start with the simplest. Good old favorite rectilinear and uniform movement.
Kinematic formulas:
Of course, let's not forget about the movement in a circle, and then move on to the dynamics and Newton's laws.
After the dynamics, it's time to consider the conditions for the equilibrium of bodies and liquids, i.e. statics and hydrostatics
Now we give the basic formulas on the topic "Work and energy". Where would we be without them!
Basic formulas of molecular physics and thermodynamics
Let's finish the section of mechanics with formulas for vibrations and waves and move on to molecular physics and thermodynamics.
Efficiency, Gay-Lussac's law, the Clapeyron-Mendeleev equation - all these sweet formulas are collected below.
By the way! There is a discount for all our readers 10% on .
Basic formulas in physics: electricity
It's time to move on to electricity, although thermodynamics loves it less. Let's start with electrostatics.
And, to the drum roll, we finish with the formulas for Ohm's law, electromagnetic induction and electromagnetic oscillations.
That's all. Of course, a whole mountain of formulas could be given, but this is useless. When there are too many formulas, you can easily get confused, and then completely melt the brain. We hope that our cheat sheet of basic formulas in physics will help you solve your favorite problems faster and more efficiently. And if you want to clarify something or have not found the formula you need: ask the experts student service. Our authors keep hundreds of formulas in their heads and click tasks like nuts. Contact us, and soon any task will be "too tough" for you.
Kinematics
Path with uniform motion:
moving S(distance in a straight line between the start and end point of movement) is usually found from geometric considerations. The coordinate during uniform rectilinear motion changes according to the law (similar equations are obtained for the remaining coordinate axes):
Average travel speed:
Average travel speed:
Having expressed the final speed from the formula above, we get a more common form of the previous formula, which now expresses the dependence of speed on time with uniformly accelerated motion:
Average speed at uniformly accelerated motion:
Displacement during uniformly accelerated rectilinear motion can be calculated using several formulas:
Coordinate with uniformly accelerated motion changes according to the law:
Velocity projection for uniformly accelerated motion changes according to the following law:
The speed at which a body falling from a height will fall h without initial speed:
Time of body fall from height h without initial speed:
The maximum height to which a body is thrown vertically upwards with an initial velocity v 0 , the time for this body to rise to its maximum height, and the total flight time (until returning to the starting point):
The time of the body falling during a horizontal throw from a height H can be found using the formula:
Range of flight of the body during a horizontal throw from a height H:
Full speed at an arbitrary point in time with a horizontal throw, and the angle of inclination of the speed to the horizon:
Maximum lifting height when throwing at an angle to the horizon (relative to the initial level):
Time to climb to maximum height when throwing at an angle to the horizon:
Flight range and total flight time of a body thrown at an angle to the horizon (provided that the flight ends at the same height from which it started, i.e. the body was thrown, for example, from ground to ground):
Determination of the rotation period for uniform circular motion:
Determining the rotational speed with uniform motion in a circle:
Relationship between period and frequency:
The linear speed with uniform motion in a circle can be found by the formulas:
Angular speed of rotation with uniform motion in a circle:
Relationship between linear and speed and angular speed expressed by the formula:
Relation between the angle of rotation and the path for uniform motion along a circle with a radius R(actually, it's just a formula for arc length from geometry):
centripetal acceleration is according to one of the formulas:
Dynamics
Newton's second law:
Here: F- the resultant force, which is equal to the sum of all forces acting on the body:
Newton's second law in projections on the axis(it is this form of notation that is most often used in practice):
Newton's third law (the force of action is equal to the force of reaction):
Elastic force:
The total stiffness coefficient of parallel connected springs:
The total stiffness coefficient of series-connected springs:
Sliding friction force (or maximum value of static friction force):
Law of gravity:
If we consider a body on the surface of the planet and enter the following notation:
Where: g is the acceleration of free fall on the surface of a given planet, then we obtain the following formula for gravity:
The free fall acceleration at a certain height from the surface of the planet is expressed by the formula:
Satellite speed in a circular orbit:
First cosmic speed:
Kepler's law for the periods of revolution of two bodies revolving around the same attracting center:
Statics
The moment of force is determined using the following formula:
Condition under which the body will not rotate:
The coordinate of the center of gravity of the system of bodies (similar equations for the remaining axes):
Hydrostatics
The definition of pressure is given by the following formula:
The pressure that creates a column of liquid is found by the formula:
But often atmospheric pressure must also be taken into account, then the formula for the total pressure at a certain depth h in liquid takes the form:
Ideal hydraulic press:
Any hydraulic press:
Efficiency for a non-ideal hydraulic press:
Strength of Archimedes(buoyant force, V- the volume of the immersed part of the body):
Pulse
body momentum is found according to the following formula:
Change in the momentum of a body or system of bodies (note that the difference between the final and initial momentum is vector):
The total momentum of the system of bodies (it is important that the sum is vector):
Newton's second law in impulsive form can be written as the following formula:
Law of conservation of momentum. As follows from the previous formula, if the system of bodies is not affected by external forces, or the action of external forces is compensated (the resultant force is zero), then the change in momentum is zero, which means that the total momentum of the system is preserved:
If external forces do not act only along one of the axes, then the projection of the momentum on this axis is preserved, for example:
work, power, energy
mechanical work is calculated using the following formula:
The most general formula for power(if the power is variable, then the average power is calculated using the following formula):
Instant Mechanical Power:
Efficiency factor (COP) can be calculated both in terms of power and work:
Potential energy of a body raised to a height:
Potential energy of a stretched (or compressed) spring:
Total mechanical energy:
Relationship between the total mechanical energy of a body or system of bodies and the work of external forces:
The law of conservation of mechanical energy (hereinafter - LSE). As follows from the previous formula, if external forces do not perform work on a body (or system of bodies), then its (their) total total mechanical energy remains constant, while energy can flow from one type to another (from kinetic to potential or vice versa) :
Molecular physics
The chemical amount of a substance is found according to one of the formulas:
The mass of one molecule of a substance can be found using the following formula:
Relationship between mass, density and volume:
The basic equation of the molecular kinetic theory (MKT) of an ideal gas is:
The definition of concentration is given by the following formula:
There are two formulas for the root-mean-square velocity of molecules:
The average kinetic energy of the translational motion of one molecule:
The Boltzmann constant, the Avogadro constant and the universal gas constant are related as follows:
Consequences from the basic equation of the MKT:
The equation of state of an ideal gas (Clapeyron-Mendeleev equation):
gas laws. Boyle-Mariotte Law:
Gay-Lussac's law:
Charles' Law:
Universal gas law (Clapeyron):
Gas mixture pressure (Dalton's law):
Thermal expansion of tel. The thermal expansion of gases is described by the Gay-Lussac law. The thermal expansion of liquids obeys the following law:
To expand solids, three formulas are used that describe the change in linear dimensions, area and volume of a body:
Thermodynamics
The amount of heat (energy) required to heat a certain body (or the amount of heat released when the body cools) is calculated by the formula:
Heat capacity ( WITH- large) of the body can be calculated through the specific heat capacity ( c- small) substances and body weight according to the following formula:
Then the formula for the amount of heat required to heat the body, or released when the body cools, can be rewritten as follows:
Phase transformations. When vaporization is absorbed, and during condensation, the amount of heat is released equal to:
During melting, it is absorbed, and during crystallization, an amount of heat is released equal to:
When fuel is burned, the amount of heat released is:
Heat balance equation (HSE). For a closed system of bodies, the following is true (the sum of the given heats is equal to the sum of the received ones):
If all heats are written taking into account the sign, where “+” corresponds to the energy received by the body, and “–” to the release, then this equation can be written as:
Work of an ideal gas:
If the gas pressure changes, then the work of the gas is considered as the area of \u200b\u200bthe figure under the graph in p–V coordinates. Internal energy of an ideal monatomic gas:
The change in internal energy is calculated by the formula:
The first law (first law) of thermodynamics (ZSE):
For various isoprocesses, formulas can be written by which the resulting heat can be calculated Q, change in internal energy Δ U and gas work A. Isochoric process ( V= const):
Isobaric process ( p= const):
Isothermal process ( T= const):
adiabatic process ( Q = 0):
The efficiency of a heat engine can be calculated using the formula:
Where: Q 1 - the amount of heat received by the working fluid in one cycle from the heater, Q 2 - the amount of heat transferred by the working fluid in one cycle to the refrigerator. Work done by a heat engine in one cycle:
The highest efficiency at given heater temperatures T 1 and refrigerator T 2 is achieved if the heat engine operates according to the Carnot cycle. This Carnot cycle efficiency equals:
Absolute humidity is calculated as the density of water vapor (the ratio of mass to volume is expressed from the Clapeyron-Mendeleev equation and the following formula is obtained):
Relative humidity can be calculated using the following formulas:
Potential energy of the liquid surface area S:
Surface tension force acting on a section of the liquid boundary with a length L:
The height of the liquid column in the capillary:
When fully wet θ = 0°, cos θ = 1. In this case, the height of the liquid column in the capillary becomes equal to:
With complete wetting θ = 180°, cos θ = –1 and, therefore, h < 0. Уровень несмачивающей жидкости в капилляре опускается ниже уровня жидкости в сосуде, в которую опущен капилляр.
Electrostatics
Electric charge can be found using the formula:
Linear charge density:
Surface charge density:
Bulk charge density:
Coulomb's Law(strength of electrostatic interaction of two electric charges):
Where: k- some constant electrostatic coefficient, which is defined as follows:
The electric field strength is found by the formula (although more often this formula is used to find the force acting on a charge in a given electric field):
The principle of superposition for electric fields (the resulting electric field is equal to the vector sum of the electric fields of its constituents):
The strength of the electric field created by the charge Q on distance r from your center:
The electric field strength created by the charged plane:
Potential energy of interaction of two electric charges expressed by the formula:
Electrical voltage is simply a potential difference, i.e. the definition of electrical voltage can be given by the formula:
In a uniform electric field, there is a relationship between field strength and voltage:
The work of the electric field can be calculated as the difference between the initial and final potential energy of the system of charges:
The work of the electric field in the general case can also be calculated using one of the formulas:
In a uniform field, when a charge moves along its lines of force, the work of the field can also be calculated using the following formula:
The definition of the potential is given by the expression:
The potential created by a point charge or a charged sphere:
The principle of superposition for the electric potential (the resulting potential is equal to the scalar sum of the potentials of the fields that make up the final field):
The following is true for the permittivity of a substance:
The definition of electric capacitance is given by the formula:
Capacitance of a flat capacitor:
Capacitor charge:
Electric field strength inside a flat capacitor:
The force of attraction of the plates of a flat capacitor:
Capacitor energy(generally speaking, this is the energy of the electric field inside the capacitor):
Volumetric energy density of the electric field:
Electricity
Current strength can be found using the formula:
current density:
Conductor resistance:
The dependence of the conductor resistance on temperature is given by the following formula:
Ohm's law(expresses the dependence of current strength on electrical voltage and resistance):
Patterns of serial connection:
Patterns of parallel connection:
The electromotive force of the current source (EMF) is determined using the following formula:
Ohm's law for a complete circuit:
The voltage drop in the external circuit is then (it is also called the voltage at the source terminals):
Short circuit current:
The work of electric current (Joule-Lenz law). Job A electric current flowing through a conductor with resistance is converted into heat Q that stands out on the conductor:
Electric current power:
Closed circuit energy balance
Useful power or power released in the external circuit:
The maximum possible useful power of the source is achieved if R = r and is equal to:
If, when connected to the same current source of different resistances R 1 and R 2 equal powers are allocated to them, then the internal resistance of this current source can be found by the formula:
Power loss or power inside the current source:
The total power developed by the current source:
Current source efficiency:
Electrolysis
Weight m substance released at the electrode is directly proportional to the charge Q passed through the electrolyte:
the value k called the electrochemical equivalent. It can be calculated using the formula:
Where: n is the valence of the substance, N A is the Avogadro constant, M is the molar mass of the substance, e is the elementary charge. Sometimes the following notation for the Faraday constant is also introduced:
Magnetism
Amp power, acting on a current-carrying conductor placed in a uniform magnetic field, is calculated by the formula:
The moment of forces acting on the frame with current:
Lorentz force, acting on a charged particle moving in a uniform magnetic field, is calculated by the formula:
The radius of the flight path of a charged particle in a magnetic field:
Induction module B magnetic field of a straight conductor with current I on distance R from it is expressed by the ratio:
Field induction at the center of a coil with a current of radius R:
inside solenoid length l and with the number of turns N a uniform magnetic field is created with induction:
The magnetic permeability of a substance is expressed as follows:
magnetic flux Φ across the square S the contour is called the value given by the formula:
EMF induction calculated by the formula:
When moving the conductor length l in a magnetic field B with speed v an EMF of induction also arises (the conductor moves in a direction perpendicular to itself):
The maximum value of the induction emf in a circuit consisting of N turns, area S, rotating with angular velocity ω in a magnetic field with induction IN:
Coil inductance:
Where: n- concentration of turns per unit length of the coil:
The relationship between the inductance of the coil, the strength of the current flowing through it and its own magnetic flux penetrating it, is given by the formula:
EMF self-induction generated in the coil:
coil energy(generally speaking, this is the energy of the magnetic field inside the coil):
Volumetric energy density of the magnetic field:
fluctuations
An equation describing physical systems capable of performing harmonic oscillations with a cyclic frequency ω 0:
The solution of the previous equation is the equation of motion for harmonic oscillations and has the form:
The oscillation period is calculated by the formula:
Oscillation frequency:
Cyclic oscillation frequency:
The dependence of speed on time for harmonic mechanical vibrations is expressed by the following formula:
Maximum speed value for harmonic mechanical vibrations:
Dependence of acceleration on time for harmonic mechanical vibrations:
Maximum acceleration value for mechanical harmonic vibrations:
The cyclic oscillation frequency of a mathematical pendulum is calculated by the formula:
Oscillation period of a mathematical pendulum:
The cyclic oscillation frequency of the spring pendulum:
Oscillation period of a spring pendulum:
The maximum value of the kinetic energy for mechanical harmonic vibrations is given by the formula:
The maximum value of potential energy for mechanical harmonic oscillations of a spring pendulum:
The relationship of the energy characteristics of the mechanical oscillatory process:
Energy characteristics and their relationship with oscillations in the electrical circuit:
The period of harmonic oscillations in an electric oscillatory circuit is determined by the formula:
Cyclic oscillation frequency in an electric oscillatory circuit:
The dependence of the charge on the capacitor on time during oscillations in the electric circuit is described by the law:
The dependence of the electric current flowing through the inductor on time during oscillations in the electrical circuit:
The dependence of the voltage on the capacitor on time during oscillations in the electrical circuit:
The maximum value of the current strength during harmonic oscillations in the electrical circuit can be calculated by the formula:
The maximum value of the voltage on the capacitor during harmonic oscillations in the electrical circuit:
Alternating current is characterized by the effective values of the current and voltage, which are associated with the amplitude values of the corresponding quantities as follows. Effective current value:
Effective voltage value:
AC power:
Transformer
If the voltage at the input to the transformer is U 1 , and at the output U 2, while the number of turns in the primary winding is n 1 , and in the secondary n 2 , then the following relation holds:
The transformation ratio is calculated by the formula:
If the transformer is ideal, then the following relationship holds (the input and output powers are equal):
In a non-ideal transformer, the concept of efficiency is introduced:
Waves
The wavelength can be calculated using the formula:
The phase difference between oscillations of two points of the wave, the distance between which l:
The speed of an electromagnetic wave (including light) in a certain medium:
The speed of an electromagnetic wave (including light) in vacuum is constant and equal to With= 3∙10 8 m/s, it can also be calculated by the formula:
The velocities of an electromagnetic wave (including light) in a medium and in a vacuum are also related to each other by the formula:
In this case, the refractive index of a certain substance can be calculated using the formula:
Optics
The optical path length is given by:
Optical path difference of two beams:
Interference maximum condition:
Interference minimum condition:
The law of refraction of light at the boundary of two transparent media:
Constant value n 21 is called the relative refractive index of the second medium relative to the first. If n 1 > n 2 , then the phenomenon of total internal reflection is possible, while:
Linear magnification lens Γ called the ratio of the linear dimensions of the image and the object:
Atomic and nuclear physics
quantum energy electromagnetic wave (including light) or, in other words, photon energy calculated by the formula:
Photon momentum:
Einstein's formula for the external photoelectric effect (EPE):
The maximum kinetic energy of emitted electrons during the photoelectric effect can be expressed in terms of the delay voltage U h and elementary charge e:
There is a cut-off frequency or wavelength of light (called the red photoelectric effect limit) such that light with a lower frequency or longer wavelength cannot cause the photoelectric effect. These values are related to the work function value by the following relation:
Bohr's second postulate or frequency rule(ZSE):
In the hydrogen atom, the following relations are satisfied that relate the radius of the trajectory of an electron rotating around the nucleus, its speed and energy in the first orbit with similar characteristics in other orbits:
On any orbit in a hydrogen atom, the kinetic ( TO) and potential ( P) the electron energies are related to the total energy ( E) by the following formulas:
The total number of nucleons in the nucleus is equal to the sum of the number of protons and neutrons:
Mass Defect:
The binding energy of the nucleus, expressed in SI units:
The binding energy of the nucleus expressed in MeV (where the mass is taken in atomic units):
Law of radioactive decay:
Nuclear reactions
For an arbitrary nuclear reaction described by a formula of the form:
The following conditions are met:
The energy yield of such a nuclear reaction is then:
Fundamentals of the special theory of relativity (SRT)
Relativistic length contraction:
Relativistic lengthening of the event time:
Relativistic law of addition of velocities. If two bodies are moving towards each other, then their speed of approach is:
Relativistic law of addition of velocities. If the bodies move in the same direction, then their relative speed:
Resting energy of the body:
Any change in body energy means a change in body mass and vice versa:
Total body energy:
Total body energy E is proportional to the relativistic mass and depends on the speed of the moving body, in this sense the following relations are important:
Relativistic mass increase:
Kinetic energy of a body moving with relativistic speed:
There is a relationship between the total energy of the body, rest energy and momentum:
Uniform circular motion
As an addition, in the table below we present all possible relationships between the characteristics of a body rotating uniformly around a circle ( T- period N- number of turns v– frequency, R is the radius of the circle, ω - angular speed, φ - angle of rotation (in radians), υ is the linear velocity of the body, a n- centripetal acceleration L- the length of the arc of the circle, t- time):
Extended PDF version of the document "All the main formulas in school physics":
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How to successfully prepare for the CT in Physics and Mathematics?
In order to successfully prepare for the CT in Physics and Mathematics, among other things, three critical conditions must be met:
- Study all the topics and complete all the tests and tasks given in the study materials on this site. To do this, you need nothing at all, namely: to devote three to four hours every day to preparing for the CT in physics and mathematics, studying theory and solving problems. The fact is that the DT is an exam where it is not enough just to know physics or mathematics, you also need to be able to quickly and without failures solve a large number of problems on various topics and varying complexity. The latter can only be learned by solving thousands of problems.
- Learn all formulas and laws in physics, and formulas and methods in mathematics. In fact, it is also very simple to do this, there are only about 200 necessary formulas in physics, and even a little less in mathematics. In each of these subjects there are about a dozen standard methods for solving problems of a basic level of complexity, which can also be learned, and thus, completely automatically and without difficulty, solve most of the digital transformation at the right time. After that, you will only have to think about the most difficult tasks.
- Attend all three stages of rehearsal testing in physics and mathematics. Each RT can be visited twice to solve both options. Again, on the CT, in addition to the ability to quickly and efficiently solve problems, and the knowledge of formulas and methods, it is also necessary to be able to properly plan time, distribute forces, and most importantly fill out the answer form correctly, without confusing either the numbers of answers and tasks, or your own name. Also, during the RT, it is important to get used to the style of posing questions in tasks, which may seem very unusual to an unprepared person on the DT.
Successful, diligent and responsible fulfillment of these three points, as well as responsible study of the final training tests, will allow you to show an excellent result on the CT, the maximum of what you are capable of.
Found an error?
If you, as it seems to you, have found an error in the training materials, then please write about it by e-mail (). In the letter, indicate the subject (physics or mathematics), the name or number of the topic or test, the number of the task, or the place in the text (page) where, in your opinion, there is an error. Also describe what the alleged error is. Your letter will not go unnoticed, the error will either be corrected, or you will be explained why it is not a mistake.
Cheat sheet with formulas in physics for the exam
Cheat sheet with formulas in physics for the exam
And not only (may need 7, 8, 9, 10 and 11 classes). For starters, a picture that can be printed in a compact form.
And not only (may need 7, 8, 9, 10 and 11 classes). For starters, a picture that can be printed in a compact form.
A cheat sheet with formulas in physics for the Unified State Examination and not only (grades 7, 8, 9, 10 and 11 may need it).
and not only (may need 7, 8, 9, 10 and 11 classes).
And then the Word file, which contains all the formulas to print them, which are at the bottom of the article.
Mechanics
- Pressure P=F/S
- Density ρ=m/V
- Pressure at the depth of the liquid P=ρ∙g∙h
- Gravity Ft=mg
- 5. Archimedean force Fa=ρ w ∙g∙Vt
- Equation of motion for uniformly accelerated motion
X=X0 + υ 0∙t+(a∙t 2)/2 S=( υ 2 -υ 0 2) /2а S=( υ +υ 0) ∙t /2
- Velocity equation for uniformly accelerated motion υ =υ 0 +a∙t
- Acceleration a=( υ -υ 0)/t
- Circular speed υ =2πR/T
- Centripetal acceleration a= υ 2/R
- Relationship between period and frequency ν=1/T=ω/2π
- Newton's II law F=ma
- Hooke's law Fy=-kx
- Law of universal gravitation F=G∙M∙m/R 2
- The weight of a body moving with acceleration a P \u003d m (g + a)
- The weight of a body moving with acceleration a ↓ P \u003d m (g-a)
- Friction force Ffr=µN
- Body momentum p=m υ
- Force impulse Ft=∆p
- Moment M=F∙ℓ
- Potential energy of a body raised above the ground Ep=mgh
- Potential energy of elastically deformed body Ep=kx 2 /2
- Kinetic energy of the body Ek=m υ 2 /2
- Work A=F∙S∙cosα
- Power N=A/t=F∙ υ
- Efficiency η=Ap/Az
- Oscillation period of the mathematical pendulum T=2π√ℓ/g
- Oscillation period of a spring pendulum T=2 π √m/k
- The equation of harmonic oscillations Х=Хmax∙cos ωt
- Relationship of the wavelength, its speed and period λ= υ T
Molecular physics and thermodynamics
- Amount of substance ν=N/ Na
- Molar mass M=m/ν
- Wed. kin. energy of monatomic gas molecules Ek=3/2∙kT
- Basic equation of MKT P=nkT=1/3nm 0 υ 2
- Gay-Lussac law (isobaric process) V/T =const
- Charles' law (isochoric process) P/T =const
- Relative humidity φ=P/P 0 ∙100%
- Int. ideal energy. monatomic gas U=3/2∙M/µ∙RT
- Gas work A=P∙ΔV
- Boyle's law - Mariotte (isothermal process) PV=const
- The amount of heat during heating Q \u003d Cm (T 2 -T 1)
- The amount of heat during melting Q=λm
- The amount of heat during vaporization Q=Lm
- The amount of heat during fuel combustion Q=qm
- The equation of state for an ideal gas is PV=m/M∙RT
- First law of thermodynamics ΔU=A+Q
- Efficiency of heat engines η= (Q 1 - Q 2) / Q 1
- Ideal efficiency. engines (Carnot cycle) η \u003d (T 1 - T 2) / T 1
Electrostatics and electrodynamics - formulas in physics
- Coulomb's law F=k∙q 1 ∙q 2 /R 2
- Electric field strength E=F/q
- Email tension. field of a point charge E=k∙q/R 2
- Surface charge density σ = q/S
- Email tension. fields of the infinite plane E=2πkσ
- Dielectric constant ε=E 0 /E
- Potential energy of interaction. charges W= k∙q 1 q 2 /R
- Potential φ=W/q
- Point charge potential φ=k∙q/R
- Voltage U=A/q
- For a uniform electric field U=E∙d
- Electric capacity C=q/U
- Capacitance of a flat capacitor C=S∙ ε ∙ε 0/d
- Energy of a charged capacitor W=qU/2=q²/2С=CU²/2
- Current I=q/t
- Conductor resistance R=ρ∙ℓ/S
- Ohm's law for the circuit section I=U/R
- The laws of the last compounds I 1 \u003d I 2 \u003d I, U 1 + U 2 \u003d U, R 1 + R 2 \u003d R
- Parallel laws. conn. U 1 \u003d U 2 \u003d U, I 1 + I 2 \u003d I, 1 / R 1 + 1 / R 2 \u003d 1 / R
- Electric current power P=I∙U
- Joule-Lenz law Q=I 2 Rt
- Ohm's law for a complete chain I=ε/(R+r)
- Short circuit current (R=0) I=ε/r
- Magnetic induction vector B=Fmax/ℓ∙I
- Ampere Force Fa=IBℓsin α
- Lorentz force Fл=Bqυsin α
- Magnetic flux Ф=BSсos α Ф=LI
- Law of electromagnetic induction Ei=ΔФ/Δt
- EMF of induction in moving conductor Ei=Вℓ υ sinα
- EMF of self-induction Esi=-L∙ΔI/Δt
- The energy of the magnetic field of the coil Wm \u003d LI 2 / 2
- Oscillation period count. contour T=2π ∙√LC
- Inductive reactance X L =ωL=2πLν
- Capacitance Xc=1/ωC
- The current value of the current Id \u003d Imax / √2,
- RMS voltage Ud=Umax/√2
- Impedance Z=√(Xc-X L) 2 +R 2
Optics
- The law of refraction of light n 21 \u003d n 2 / n 1 \u003d υ 1 / υ 2
- Refractive index n 21 =sin α/sin γ
- Thin lens formula 1/F=1/d + 1/f
- Optical power of the lens D=1/F
- max interference: Δd=kλ,
- min interference: Δd=(2k+1)λ/2
- Differential grating d∙sin φ=k λ
The quantum physics
- Einstein's formula for the photoelectric effect hν=Aout+Ek, Ek=U ze
- Red border of the photoelectric effect ν to = Aout/h
- Photon momentum P=mc=h/ λ=E/s
Physics of the atomic nucleus
- Law of radioactive decay N=N 0 ∙2 - t / T
- Binding energy of atomic nuclei
E CB \u003d (Zm p + Nm n -Mya)∙c 2
ONE HUNDRED
- t \u003d t 1 / √1-υ 2 / c 2
- ℓ=ℓ 0 ∙√1-υ 2 /c 2
- υ 2 \u003d (υ 1 + υ) / 1 + υ 1 ∙υ / c 2
- E = m With 2
