1) moving in a straight line at a uniform speed

1. Acceleration A = (vt-Vo)/tWith Vo as the positive direction, A and VO are in the same direction (accelerating) a>0; On the other hand, a < 0

2. Terminal speed Vt=Vo+at

3. Displacement S = VOT+AT2/2 = Vping =tVt/2t.

4. Useful inference Vt2 -Vo2=2as

5. Average speed V =S/t (definition)

6. Intermediate time speed vt/2 = Vping =(Vt+Vo)/2 Intermediate position speed Vs/2=[(Vo2 +Vt2)/2] 1/2.

7. It is inferred from the experiment that δS = aT2δS is the displacement difference in adjacent consecutive equal time (t).

8. Main physical quantities and units: initial velocity (Vo):m/s acceleration (a):m/s2 terminal velocity (VT): m/s.

Time (t): second (s) Displacement (s): meter (m) Distance: meter (m) Speed unit conversion:1m/s = 3.6 km/h.

Note: (1) Average speed is vector.

(2) The acceleration is not necessarily high when the speed of the object is high.

(3)a=(Vt-Vo)/t is only a measure, not a judgment.

(4) Other related contents: particle, displacement and distance, speed and speed, S-T diagram and V-T diagram.

2) Free fall

1. Initial velocity Vo=0 2. Final speed Vt=gt.

3. Falling height h=gt2/2 4. Inference Vt2=2gh.

Note: (1) Free falling body is a uniformly accelerated linear motion with zero initial velocity, which follows the law of uniformly variable linear motion.

(2)a=g=9.8≈ 10m/s2, and the gravity acceleration near the equator is small; The poles of the earth are the largest; It is smaller on high mountains than on flat land.

3)* Throw vertically upwards

1. Displacement S=Vot- gt2/2 2. The final speed Vt= Vo- gt (g=9.8≈ 10m/s2).

3. It is useful to infer that Vt2 -Vo2=-2gS 4. Maximum lifting height Hm=Vo2/2g (from the throwing point)

5. Round trip time t=2Vo/g (time from throwing back to original position)

Note: (1) Full-course treatment: it is linear motion with uniform deceleration, with positive upward direction and negative acceleration.

(2) Sectional treatment: the upward movement is uniform deceleration, and the downward movement is free fall, which is symmetrical.

(3) The process of ascending and descending is symmetrical, for example, at the same point, the speed is equal and the direction is opposite.

Second, the motion of particles-curve motion gravity

1) flat throwing motion

1. horizontal velocity Vx=Vo 2. Vertical speed Vy=gt.

3. horizontal displacement Sx=Vot 4. Vertical displacement Sy=gt2/2.

5. Exercise time t=(2Sy/g) 1/2 (usually expressed as (2h/g) 1/2).

6. Closing speed vt = (vx2+vy2)1/2 = [VO2+(gt) 2]1/2.

The angle β between the closing speed direction and the horizontal plane: tgβ = vy/VX = gt/vo.

7. joint displacement S=(Sx2+ Sy2) 1/2,

The included angle α between the displacement direction and the horizontal plane: tgα = sy/sx = gt/2vo.

Note: (1) Flat throwing motion is a curve motion with uniform change, with acceleration of g, which can usually be regarded as the synthesis of uniform linear motion in horizontal direction and free falling motion in vertical direction.

(2) The movement time is determined by the falling height h(Sy) and has nothing to do with the horizontal throwing speed; T is the key to solving the problem of flat throwing.

(3) The relationship between α and β is tgβ=2tgα.

(4) When the velocity direction and the resultant force (acceleration) direction are not on the same straight line, the object moves in a curve; Curved motion must have acceleration.

2) Uniform circular motion

1. linear velocity v = s/t = 2π r/t = ω r 2. Angular velocity ω = φ/t = 2π/t = 2π f.

3. centripetal acceleration a=V2/R=ω2R=(2π/T)2R 4. Centripetal force f centripetal force =mV2/R=mω2R=m(2π/T)2R.

5. Period and frequency T= 1/f 6. The relationship between angular velocity and linear velocity v = ω r.

7. The relationship between angular velocity and rotational speed ω=2πf=2πn (frequency and rotational speed are the same after unified unit).

8. Main physical quantities and units: arc length (s): meter (m), angle (φ): radian (rad), frequency (f): hertz (Hz), period (t): second (s), speed (n): r/s radius (r): meter (m).

Note: (1) The centripetal force can be provided by a specific force, resultant force or component force, and the direction is always perpendicular to the speed direction.

(2) The centripetal force of an object in uniform circular motion is equal to the resultant force. The centripetal force only changes the direction of the speed, but does not change the size of the speed, so the kinetic energy of the object remains unchanged, but the momentum is constantly changing.

3) Gravity

1. Kepler's third law T2/R3=K R: orbital radius T: period K: constant (independent of planetary mass)

2. The law of universal gravitation F = GM1m2/R2g = 6.67×10-1n? The m2/kg2 direction is on their connecting line.

3. Gravity and acceleration of gravity on any celestial body: GM=gR2 (gold substitution)

M: mass of celestial body (kg); G: gravitational acceleration of celestial body surface (m/S2); R: the radius of the celestial body (m).

4. Satellite orbital velocity, angular velocity and period are all used: F universal =F centripetal.

5. The first, second and third cosmic velocities: v1= 7.9 km/SV2 =11.2 km/SV3 =16.7 km/s.

Note: (1) The centripetal force required for celestial motion is provided by gravity, and f center =F million.

(2) The mass density of celestial bodies can be estimated by applying the law of universal gravitation.

(3) Geosynchronous satellites can only run over the equator with the same period as the earth's rotation, h ≈ 36,000 km.

(4) When the orbit radius of the satellite decreases, the potential energy decreases, the kinetic energy increases, the speed increases and the period decreases.

(5) The maximum circling speed and minimum launching speed of the Earth satellite are 7.9 km/s, and the minimum period is about 83 minutes.

Three, force (general force, torque, force synthesis and decomposition)

1) ordinary force

1. Gravity: size: G=mg direction: vertical downward action point: center of gravity

G=9.8m/s2 ≈ 10 m/s2, which is suitable for near surface.

Hooke's law: F=kX direction: along the recovery deformation direction k: stiffness coefficient (N/m) X: deformation variable (m)

3. Sliding friction: f=μN direction: opposite to the relative motion direction of the object μ: friction coefficient n: positive pressure (n)

4. Static friction force 0≤f Static ≤fm direction: fm is the maximum static friction force opposite to the relative motion trend of the object.

5. Gravity F = GM1m2/R2g = 6.67×10-1/n? The m2/kg2 direction is on their connecting line.

6. Electrostatic force F = kq1Q2/R2k = 9.0×109N? The m2/C2 direction is on their connecting line.

7. electric field force F=Eq E: field strength N/C q: electric field force exerted on positive charge by electric quantity c is in the same direction as field strength.

8. Ampere force F=BILsinθ θ is the included angle between b and l when L⊥B: F=BIL and B//L: F=0.

9. Lorentz force f=qVBsinθ θ is the included angle between b and v, when V⊥B: f=qVB, when V//B: f=0.

Note: (1) The stiffness coefficient k is determined by the spring itself.

(2) The friction coefficient μ has nothing to do with pressure and contact area, but is determined by the material characteristics and surface conditions of the contact surface.

(3)fm slightly larger than μN is generally considered as FM ≈ μ n.

(4) Symbol and unit of physical quantity B: magnetic induction intensity (T), L: effective length (M), I: current intensity (A), V: charged particle velocity (m/S), Q: charged particle (charged body) electric quantity (C),

(5) Ampere force is jointly judged by "electromagnetic force" and Lorentz force direction.

2)* Torque

1. Moment M=FL L is the arm of the corresponding force, which refers to the vertical distance from the line of action of the force to the rotating shaft (point).

2. Rotational balance condition M clockwise = M counterclockwise M is n? I'm here, n? m≠J

3) Composition and decomposition of forces

1. The resultant force on the same straight line has the same direction: f = f1+F2; Opposite direction: f = f1-F2 (f1> F2)

2. Synthesis of mutually angled forces

f =(f 12+f22+2f 1 F2 cosα) 1/2f 1⊥F2:f =(f 12+f22) 1/2。

3. resultant force range | f1-F2 |≤ f≤| f1+F2 |

4. Orthogonal decomposition of force: FX = FCOS β FY = FSIN β is the included angle between the resultant force and the X axis tgβ=Fy/Fx.

Note: The synthesis and decomposition of (1) force (vector) follows the parallelogram law.

(2) The relationship between resultant force and components is equivalent substitution, and resultant force can replace the joint action of components, and vice versa.

(3) In addition to the formula method, it can also be solved by drawing method. At this time, the scale should be selected for strict drawing.

(4) When the values of F 1 and F2 are constant, the greater the included angle (α angle) of F 1 and F2, the smaller the resultant force.

(5) The combination of forces on the same straight line can take the positive direction along the straight line, and the direction of forces is expressed by symbols, which can be transformed into algebraic operation.

Four. Dynamics (motion and force)

1. the first law of motion (law of inertia): an object has inertia and always keeps a state of uniform linear motion.

1, Hooke's law: F = kx (x is elongation or compression; K is the stiffness coefficient, which is only related to the original length, thickness and material of the spring)

2. Gravity: G = mg (g varies with the height, latitude and geological structure above the ground; Gravity is about equal to the gravity of the earth on the ground)

3. Find the resultant force of f sum: use the parallelogram rule.

Note: The composition and decomposition of (1) force follow the parallelogram law.

(2) The resultant force range of the two forces:? F 1-F2 F？ F 1 + F2

(3) The resultant force can be greater than, less than or equal to the component force.

4. Two equilibrium conditions:

(1) The equilibrium condition of an object under the combined force: the combined force is zero when the object is at rest or moving in a straight line at a constant speed.

F =0 or: Fx =0 Fy =0.

Inference: [1] If three non-parallel forces act on an object and are balanced, then these three forces must be shared.

[2] Three concurrent forces act on an object in balance, in which the resultant force of any two forces is equal in magnitude and opposite in direction to the third force.

(2? ) The equilibrium condition of an object with a fixed axis of rotation: the algebraic sum of moments is zero. (Just need to know)

Torque: M=FL (L is the arm of force and the vertical distance from the rotating shaft to the line of force)

5, the formula of friction:

(1) sliding friction: f=? [Mathematics] Function

Description: ① FN is the elastic force between contact surfaces, which can be greater than g; It can also be equal to g; It can also be less than g.

② ? Is the sliding friction coefficient, which is only related to the material and roughness of the contact surface, and has nothing to do with the size of the contact area, the relative motion speed of the contact surface and the positive pressure n.

(2) Static friction: Its magnitude is related to other forces, which is solved by the equilibrium condition of the object or Newton's second law, and is not proportional to the positive pressure.

Size range: o? F Jing? Fm (fm is the maximum static friction, which is related to positive pressure)

Description:

A, friction can be the same as the direction of motion, can also be opposite to the direction of motion.

B. Friction can do positive work, negative work or no work.

C the direction of friction is opposite to the direction of relative motion between objects or the direction of relative motion trend.

D, stationary objects will be affected by sliding friction, and moving objects will also be affected by static friction.

6. buoyancy: F=? Attention unit

7. Gravity: F=G

(1) Applicable conditions: the attraction between two particles (or it can be regarded as particles, such as two uniform spheres).

(2) G is the gravitational constant, which was first measured by Cavendish with a torsion balance device.

(3) Application in celestial bodies: (m- celestial body mass, m- satellite mass, r- celestial body radius, g- gravitational acceleration of celestial body surface, height from h- satellite to celestial body surface)

First, gravity = centripetal force

G

B, near the surface of the earth, gravity = gravity.

Mg = gram = gram

C, the first cosmic velocity

mg = m V=

Coulomb force: F=K (applicable condition: force between two charges in vacuum)

9. Electric field force: f = eq (the direction of f and electric field strength can be the same or opposite).

10, magnetic field force:

(1) Lorentz force: the force of a magnetic field on a moving charge.

Formula: f=qVB (B? V) direction-left hand rule

(2) Ampere force: the acting force of magnetic field on current.

Formula: F= BIL (B? I) direction-left hand rule

1 1, Newton's second law: f = ma or? Fx = m ax？ Fy = m ay

Scope of application: Macroscopic low-speed objects.

Understanding: (1) Vector (2) Instantaneity (3) Independence

Homogeneity homogeneity homogeneity homogeneity

12, uniform linear motion:

Basic law: Vt = V0+a t S = vo t+a t2.

Several important inferences:

(1) VT2-V02 = 2as (uniformly accelerated linear motion: A is positive, uniformly decelerated linear motion: A is positive)

(2) Instantaneous velocity at the intermediate moment of section 2)ab:

Vt/2 = = (3) Instantaneous velocity of the displacement midpoint of AB section:

Vs/2 =

Uniform speed: vt/2 = vs/2; Uniform acceleration or uniform deceleration linear motion: vt/2

(4) uniformly accelerated linear motion with zero initial velocity, at 1s, 2s, 3s? The displacement ratio within ……ns is12: 22: 32 ... N2; 1s, the displacement ratio in 2s and 3s ... ns is1:3: 5 ... (2n-1); 1 meter time ratio, the second meter, the third meter ... the nth meter is 1: ...

(5) No matter whether the initial velocity is zero or not, the displacement difference of a particle moving in a straight line at a uniform speed in consecutive adjacent equal time intervals is constant:? S = at2(a- acceleration of uniform linear motion t- time of each time interval)

13, vertical throwing motion: the rising process is a uniform deceleration linear motion, and the falling process is a uniform acceleration linear motion. The whole process is that the initial velocity is VO and the acceleration is? Uniform deceleration linear motion of g.

(1) Maximum rising height: H =

(2) Rise time: t=

(3) When ascending and descending through the same position, the acceleration is the same, but the speed is equivalent to the opposite.

(4) The time of rising and falling through the same displacement is equal. Time from throwing to falling back: t =

(5) Formula applicable to the whole process: S = VOT-GT2VT = VO-GTT.

Vt2-VO2 =-2 GS (understanding the sign of S and Vt)

14, uniform circular motion formula

Linear speed: V= R? =2 f R=

Angular velocity:? =

Centripetal acceleration: a = 2 f2 R

Centripetal force: f = ma = M2R = mmm4n2r.

Note: (1) The centripetal force of an object in uniform circular motion is the resultant force on the object and always points to the center of the circle.

(2) The centripetal force of the uniform circular motion of the satellite around the earth and the planet around the sun is provided by gravity.

(3) The centripetal force of the electrons outside the hydrogen nucleus moving in a uniform circle is provided by the coulomb force of the nucleus to the electrons outside the nucleus.

15. Flat throwing motion formula: the combination of uniform linear motion and uniform acceleration linear motion, with initial velocity of zero.

Horizontal component motion: horizontal displacement: x= vo t Horizontal component velocity: vx = vo.

Vertical component motion: vertical displacement: y = g t2 vertical component velocity: vy= g t.

tg？ = Vy = Votg？ Vo =Vyctg？

V = Vo = Vcos？ Vy = Vsin？

In Vo, Vy, v, x, y, t, If any two of the seven physical quantities are known, five other physical quantities can be obtained according to the above formula.

16, momentum and impulse: momentum: P = mV impulse: I = F t

(attention vector)

17, momentum theorem: the impulse of the resultant force of external forces on an object is equal to the change of its momentum.

Formula: f and t = mv'-mv (stress analysis and positive direction are the key points in solving problems)

18, Law of Conservation of Momentum: If the interacting object systems are not subjected to external forces or the sum of the external forces is zero, their total momentum remains unchanged. (Research object: two or more interactive objects)

Formula: m1v1+m2v2 = m1v1'+m2v2' or? p 1 =-？ P2 or? p 1 +？ p2 = 0

Applicable conditions:

(1) The system is not affected by external force. (2) The system is subjected to external force, but the resultant force is zero.

(3) When the system is subjected to external force, the resultant force is not zero, but it is far less than the interaction force between objects.

(4) The resultant force of the system in a certain direction is zero, and the momentum in that direction is conserved.

19, work: W = Fs cos? (Applicable to the calculation of constant force work)

(1) Understanding Positive Work, Negative Work and Negative Work

(2) Work is a measure of energy conversion.

Gravitational work. Measurement. Variation of gravitational potential energy.

Work done by electric field force-measurement-change of electric potential energy

Work-measurement of molecular force-change of molecular potential energy

Work done by external force-measurement-kinetic energy change.

20. kinetic energy and potential energy: kinetic energy: Ek =

Gravitational potential energy: Ep = mgh (related to the selection of zero potential energy surface)

2 1, kinetic energy theorem: the total work done by external force is equal to the change (increment) of the kinetic energy of the object.

Formula: w =? Ek = Ek2-Ek 1 = 22. Law of conservation of mechanical energy: mechanical energy = kinetic energy+gravitational potential energy+elastic potential energy.

Condition: The system only has internal gravity or elasticity to do work.

Formula: mgh 1+or? Ep MINUS =? Ek increase

23. Conservation of energy (relationship between work and energy conversion): In a system with mutual friction, the reduced mechanical energy is equal to the work done by friction.

E = Q = f S phase

24. Power: p = (average power of internal force acting on the object in t time)

P = FV (F is traction, not resultant force; When v is instantaneous speed, p is instantaneous power; When v is the average speed, p is the average power; When p is constant, f is proportional to v)

25. Simple harmonic vibration: restoring force: F = -KX acceleration: a =-

Formula of period of simple pendulum: T= 2 (independent of pendulum mass and amplitude)

(Do you understand? ) Periodic formula of spring oscillator: T= 2 (related to oscillator mass and spring stiffness coefficient, but not to amplitude)

26. the relationship between wavelength, wave velocity and frequency: V = =? F (for all waves)