S: distance t: time
Gravity G(N)G = mg
M: quality
G: gravitational acceleration, constant, 9.8N/kg or 10N/kg.
Density ρ(kg/m3)ρ=m/v
M: quality
Five: volume
The resultant force f and (n) are in the same direction: f and =F 1+F2.
Opposite direction: F =F 1-F2 When the direction is opposite, f1> Second generation
Buoyancy f float (N)F float =G object -G line of sight g line of sight: gravity of objects in liquid.
Buoyancy f float (N)F float =G object
This formula only applies to floating or suspended objects.
Buoyancy F float (N)F float =G row =m row g=ρ liquid gV row
Row G: The gravity of the liquid shifts.
Line m: mass of displacement liquid.
ρ liquid: density of liquid
Line V: Volume of liquid discharged (i.e. volume immersed in liquid).
Lever balance condition f1L 1 = f2l2f1:power l1:power arm.
F2: resistance L2: resistance arm
Crown block F=G object
S=hF: tension applied to the free end of the rope.
G object: the gravity of the object.
S: the distance that the free end of the rope moves.
H: the rising distance of the object.
Moving pulley F=(G object +G wheel) /2
S=2hG object: the gravity of the object.
G wheel: the gravity of the moving pulley.
Pulley block F=(G object +G wheel)
S=nhn: the number of rope segments passing through the moving pulley.
Mechanical work W(J)W=Fs
F: Force.
S: distance moved in the direction of force.
Useful work = G substance h
When the pulley block is placed vertically, the total work W total W total =Fs.
Mechanical efficiency eta = wayes/wtotal×100%
Power P(w)P=w/t
Woman: Work.
T: time
Pressure p(Pa)P=F/s
pressure
stressed zone
Liquid pressure p (pa) p = rhogh
ρ: density of liquid
H: depth (vertical distance from liquid surface to required point)
Heat Q(J)Q=cm△t
C: specific heat capacity of matter
M: quality
△t: change value of temperature
Fuel combustion emission
Q(J)Q=mq。
M: quality
Q: calorific value
Common physical formulas and important knowledge points
1. Deformation physical formula (unit) formula Remarks formula
Series circuit current I (a) I = i 1 = I2 = ... Current is equal everywhere.
Series circuit voltage u (v) u = u 1+U2+ ... The series circuit acts as a voltage divider.
Series circuit resistance r (ω) r = r 1+R2+ ...
Parallel circuit current I (a) I = i 1+I2+ ... The main circuit current is equal to the sum of each branch current (shunt).
Parallel circuit voltage u (v) u = u 1 = U2 = ...
Parallel circuit resistance r (ω)1/r =1/r1+1/R2+ ...
Ohm's law I=U/I
The current in the circuit is directly proportional to the voltage and inversely proportional to the resistance.
Current definition I=Q/t
Q: Charge (Coulomb)
time
Electric work W(J)W=UIt=Pt
U: voltage I: current
T: time p: electricity
Electric power P=UI=I2R=U2/R
U: voltage I: current r: resistance
Electromagnetic wave velocity and wave
The relationship between length and frequency C=λνC: wave velocity (the wave velocity of electromagnetic wave is constant, equal to 3× 108m/s).
λ: wavelength v: frequency
Several values to remember:
A. the propagation speed of sound in the air: 340 m/sb; Propagation speed of light in vacuum or air: 3× 108 m/s/s.
Density of water: 1.0× 103kg/m3d. Specific heat capacity of water: 4.2× 103J/(kgo℃).
E. dry cell voltage:1.5vf. Household circuit voltage: 220V.
G. safe voltage: not higher than 36V.
Multiplication and factorization A2-B2 = (a+b) (a-b) A3+B3 = (a+b) (A2-AB+B2) A3-B3 = (A-B (A2+AB+B2))
Trigonometric inequality | A+B |≤| A |+B||||| A-B|≤| A |+B || A |≤ B < = > -b≤a≤b
|a-b|≥|a|-|b| -|a|≤a≤|a|
The solution of the unary quadratic equation -b+√(b2-4ac)/2a -b-√(b2-4ac)/2a
The relationship between root and coefficient x1+x2 =-b/ax1* x2 = c/a Note: Vieta theorem.
discriminant
B2-4ac=0 Note: This equation has two equal real roots.
B2-4ac >0 Note: The equation has two unequal real roots.
B2-4ac & lt； Note: The equation has no real root, but a complex number of the yoke.
formulas of trigonometric functions
Two-angle sum formula
sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinb cosa
cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)
Double angle formula
tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA
cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a
half-angle formula
sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-cosA)/2)
cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))
Sum difference product
2 Sina cosb = sin(A+B)+sin(A-B)2 cosa sinb = sin(A+B)-sin(A-B)
2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = cos(A+B)-cos(A-B)
sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)
tanA+tanB = sin(A+B)/cosa cosb tanA-tanB = sin(A-B)/cosa cosb
ctgA+ctgBsin(A+B)/Sina sinb-ctgA+ctgBsin(A+B)/Sina sinb
The sum of the first n terms of some series
1+2+3+4+5+6+7+8+9+…+n = n(n+ 1)/2 1+3+5+7+9+ 1 1+ 13+ 15+…+(2n- 1)= N2
2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6
13+23+33+43+53+63+…n3 = N2(n+ 1)2/4 1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3
Sine theorem a/sinA=b/sinB=c/sinC=2R Note: where r represents the radius of the circumscribed circle of a triangle.
Cosine Theorem b2=a2+c2-2accosB Note: Angle B is the included angle between side A and side C..
The standard equation of a circle (x-a)2+(y-b)2=r2 Note: (A, B) is the center coordinate.
General equation of circle x2+y2+Dx+Ey+F=0 Note: D2+E2-4f > 0
Parabolic standard equation y2=2px y2=-2px x2=2py x2=-2py
Lateral area of a straight prism S=c*h lateral area of an oblique prism s = c' * h.
Lateral area of a regular pyramid S= 1/2c*h' lateral area of a regular prism S= 1/2(c+c')h'
The lateral area of the frustum of a cone S = 1/2(c+c')l = pi(R+R)l The surface area of the ball S=4pi*r2.
Lateral area of cylinder S=c*h=2pi*h lateral area of cone s =1/2 * c * l = pi * r * l.
The arc length formula l=a*r a is the radian number r > of the central angle; 0 sector area formula s= 1/2*l*r
Conical volume formula V= 1/3*S*H Conical volume formula V= 1/3*pi*r2h
Oblique prism volume V=S'L Note: where s' is the straight cross-sectional area and l is the side length.
Cylinder volume formula V=s*h Cylinder V=pi*r2h 1, each copy × number of copies = total number of copies ÷ each copy = total number of copies ÷ number of copies = number of copies.
2. 1 multiple× multiple = multiple1multiple = multiple/multiple = 1 multiple
3. Speed × time = distance/speed = time/distance/time = speed
4. Unit price × quantity = total price ÷ unit price = total quantity ÷ quantity = unit price
5. Work efficiency × working hours = total workload ÷ work efficiency = working hours ÷ total workload ÷ working hours = work efficiency.
6. Appendix+Appendix = sum, and-one addend = another addend.
7. Minus-Minus = Minus-Minus = Minus+Minus = Minus
8. Factor × factor = product ÷ one factor = another factor.
9. Dividend = quotient dividend = divisor quotient × divisor = dividend
Calculation formula of mathematical graphics in primary schools
1, square c perimeter s area a side length perimeter = side length× 4c = 4a area = side length× side length s = a× a.
2. Cube V: volume A: side surface area = side length × side length× 6s table =a×a×6 volume = side length× side length× side length V = a× a× a.
3. rectangular
Perimeter area side length
Circumference = (length+width) ×2
C=2(a+b)
Area = length × width
S=ab
4. Cuboid
V: volume s: area a: length b: width h: height.
(1) Surface area (L× W+L× H+W× H) ×2
S=2(ab+ah+bh)
(2) Volume = length × width × height
V=abh
5 triangle
S area a bottom h height
Area = bottom × height ÷2
s=ah÷2
Height of triangle = area ×2÷ base.
Triangle base = area ×2÷ height
6 parallelogram
S area a bottom h height
Area = bottom × height
S = ah
7 trapezoid
Height of upper bottom b and lower bottom h in s area a
Area = (upper bottom+lower bottom) × height ÷2
s=(a+b)× h÷2
8 laps
Area c perimeter d= diameter r= radius
(1) circumference = diameter ×∏=2×∏× radius
c =∏d = 2r
(2) area = radius × radius×∈
Cylinder 9
V: volume h: height s; Bottom area r: bottom radius c: bottom perimeter
(1) lateral area = bottom circumference × height.
(2) Surface area = lateral area+bottom area ×2
(3) Volume = bottom area × height
(4) Volume = lateral area ÷2× radius.
10 cone
V: volume h: height s; Bottom area r: bottom radius
Volume = bottom area × height ÷3
Total number ÷ Total number of copies = average value
Formula of sum and difference problem
(sum+difference) ÷ 2 = large number
(sum and difference) ÷ 2 = decimal
And folding problems.
Sum \ (multiple-1) = decimal
Decimal × multiple = large number
(or sum-decimal = large number)
Difference problem
Difference ÷ (multiple-1) = decimal
Decimal × multiple = large number
(or decimal+difference = large number)
Tree planting problem
1 The problem of planting trees on unclosed lines can be divided into the following three situations:
(1) If trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes+1 = total length-1.
Total length = plant spacing × (number of plants-1)
Plant spacing = total length ÷ (number of plants-1)
2 If you want to plant trees at one end of the unclosed line and not at the other end, then:
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
(3) If no trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes-1 = total length-1.
Total length = plant spacing × (number of plants+1)
Plant spacing = total length ÷ (number of plants+1)
The quantitative relationship of planting trees on the closed line is as follows
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
The question of profit and loss
(Profit+Loss) ÷ Difference between two distributions = number of shares participating in distribution.
(Big profit-small profit) ÷ Difference between two distributions = number of shares participating in distribution.
(big loss-small loss) ÷ The difference between two distributions = the number of shares participating in the distribution.
encounter a problem
Meeting distance = speed × meeting time
Meeting time = meeting distance/speed and
Speed Sum = Meeting Distance/Meeting Time
Catch up with the problem
Catch-up distance = speed difference× catch-up time
Catch-up time = catch-up distance ÷ speed difference
Speed difference = catching distance ÷ catching time
Tap water problem
Downstream velocity = still water velocity+current velocity
Countercurrent velocity = still water velocity-current velocity
Still water velocity = (downstream velocity+countercurrent velocity) ÷2
Water velocity = (downstream velocity-countercurrent velocity) ÷2
Concentration problem
Solute weight+solvent weight = solution weight.
The weight of solute/solution × 100% = concentration.
Solution weight × concentration = solute weight
Solute weight-concentration = solution weight.
Profit and discount problem
Profit = selling price-cost
Profit rate = profit/cost × 100% = (selling price/cost-1) × 100%.
Up and down amount = principal × up and down percentage
Discount = actual selling price ÷ original selling price× 1 00% (discount <1)
Interest = principal × interest rate× time
After-tax interest = principal × interest rate × time × (1-20%)
Length unit conversion
1 km = 1 000m1m = 10 decimeter.
1 decimeter =10cm1m =10cm.
1 cm = 10/0mm
Area unit conversion
1 km2 = 100 hectare
1 ha = 1 10,000 m2
1 m2 = 100 square decimeter
1 square decimeter = 100 square centimeter
1 cm2 = 100 mm2
Volume (volume) unit conversion
1 m3 = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cubic decimeter = 1 liter
1 cm3 = 1 ml
1 m3 = 1000 liter
Weight unit conversion
1 ton = 1000 kg
1 kg =1000g
1 kg = 1 kg
Rmb unit conversion
1 yuan = 10 angle.
1 angle = 10 point
1 yuan = 100 integral.
Time unit conversion
1 century = 100 1 year =65438+ February.
The big month (3 1 day) includes:1\ 3 \ 5 \ 7 \ 8 \10 \ 65438+February.
Abortion (30 days) includes: April \ June \ September \165438+1October.
February 28th in a normal year and February 29th in a leap year.
There are 365 days in a normal year and 366 days in a leap year.
1 day =24 hours 1 hour =60 minutes.
1 minute =60 seconds 1 hour =3600 seconds.
Calculation formula of perimeter, area and volume of mathematical geometry in primary schools
1, the perimeter of the rectangle = (length+width) ×2 C=(a+b)×2.
2. The circumference of a square = side length ×4 C=4a.
3. Area of rectangle = length× width S=ab
4. Square area = side length x side length s = a.a = a.
5. Area of triangle = base × height ÷2 S=ah÷2.
6. parallelogram area = bottom x height S=ah
7. trapezoidal area = (upper bottom+lower bottom) × height ÷ 2s = (a+b) h ÷ 2.
8. Diameter = Radius× 2D = 2r Radius = Diameter ÷2 r= d÷2
9. The circumference of a circle = π× diameter = π× radius× 2c = π d = 2π r.
10, area of circle = π× radius× radius.