the motion of a particle (1)--Linear motion
1) Uniform variable speed linear motion1. Average speed v=s/t (definition)2. Useful Inferences Vt*vt-vo*vo=2as3. Intermediate time speed vt/2=v flat = (VT+VO)/24. Terminal Speed Vt=vo+at5. Intermediate position Speed vs/2=[(VO*VO+VT*VT)/2]1/26. Displacement S=v Flat t=vot+at*t/2=vt/2t7. Acceleration a= (VT-VO)/t{with Vo positive direction, a with VO (acceleration) a>0; reverse A<0}8. The experimental inference Δs=at*t{δs is the difference in the displacement of consecutive adjacent equal time (T)}9. Main physical quantity and unit: initial velocity (Vo): M/s; acceleration (a): m/s*s; end Velocity (Vt): M/S; time (t) seconds (s); displacement (s): M (m); distance: m; speed unit conversion: 1m/s=3.6km/h.
Note:(1) The average velocity is a vector;(2) object speed is large, acceleration is not necessarily large;(3) a= (VT-VO)/T is only a measure, not a decision-type;(4) Other relevant content: particle, displacement and distance, reference system, time and Moment (see Volume p19)/s–t, v–t Chart/speed and rate, instantaneous speed (see volume p24). 2) Free fall
1. Initial speed vo=0? 2. Terminal Speed VT=GT3. Drop height H=GT*T/2 (calculated from VO position)4. Inference Vt*vt=2ghNote:(1) Free fall is a linear motion with the initial velocity of zero and uniformly accelerating, and follows the rule of linear motion with uniform speed;(2) a=g=9.8m/s*s≈10m/s*s (the gravitational acceleration is smaller near the equator, smaller than the flat in the mountains, and vertically downward). (3) Vertical Upper throw motion1. Displacement S=VOT-GT*T/22. Terminal velocity vt=vo-gt (g=9.8m/s*s≈10m/s*s)3. Useful Inferences Vt*vt-vo*vo=-2gs4. Ascent Maximum height hm=vo*vo/2g (throw point count)5. Round Trip Time t=2vo/g (from the time it was thrown back to its original location)Note:(1) The whole process of processing: is the uniform deceleration linear motion, to upward for the positive direction, the acceleration to take negative value;(2) Sub-processing: upward for uniform deceleration linear motion, downward for free fall, with symmetry;(3) The rise and fall process is symmetrical, such as at the same point velocity equivalent reverse.
second, the movement of the particle (2)--curve motion, gravitation
1) Flat throw motion1. Horizontal direction speed: Vx=vo2. Vertical direction Speed: vy=gt3. Horizontal direction Displacement: X=vot4. Vertical Displacement: Y=GT*T/25. Exercise Time t= (2y/g) 1/2 (usually denoted as (2h/g) )6. Hop Speed vt= (vx*vx+vy*vy) 1/2=[vo*vo+ (GT) * (GT)]1/2 speed direction and horizontal angle β:tgβ=vy/vx=gt/v07. Combined Displacement: s= (x*x+y*y) 1/2, displacement direction and horizontal angle Α:tgα=y/x=gt/2vo8. Horizontal acceleration: ax=0; Vertical direction acceleration: ay=gNote:(1) The flat-throw motion is a uniform variable speed curve movement, the acceleration is g, usually can be regarded as horizontal direction of the uniform linear operation and vertical direction of the free fall synthesis;(2) The movement time is determined by the drop height h (y) and is independent of the horizontal throwing speed;(3) The relationship between θ and β is tgβ=2tgα;(4) the time t is the key to solve the problem in the horizontal throw motion, and (5) The object that does the curve movement must have the acceleration, when the velocity direction is not in the same line as the resultant Force (acceleration), the object does the curve motion. 2) Uniform circular motions1. Line Speed v=s/t=2πr/t2. Angular Velocity ω=φ/t=2π/t=2πf3. centripetal acceleration a=v2/r=ω2r= (2π/t) 2r4. centripetal force F-Heart =MV2/R=MΩ2R=MR (2π/t) 2=mωv=f5. Cycle and frequency: t=1/f6. The relationship between angular velocity and line velocity: v=ωr7. Angular velocity and rotational speed of the relationship ω=2πn (here the frequency and speed of the same meaning)8. Main physical quantities and units: arc length (s): M (m), Angle (Φ): radians (RAD), Frequency (f): khz (HZ), period (T): seconds (s), Speed (n): r/s, Radius (R): M (m), line Speed (V): M/s, angular velocity (ω): rad/s ; centripetal acceleration: m/s*s. Note:(1) centripetal force can be provided by some specific forces, can also be provided by the force, but also by the power supply, direction is always perpendicular to the direction of the speed, pointing to the center of the circle;(2) Do uniform circular motions object, its centripetal force equals the resultant force, and centripetal force only changes the direction of speed, does not change the speed of the size, so the kinetic energy of the object remains unchanged, centripetal force does not work, but momentum is constantly changing. 3) Gravitation
1. Kepler's third law: T2/r3=k (=4Π2/GM) {R: Orbital radius, T: period, K: constant (independent of planet Mass, depending on the mass of the Center object)} 2. Law of universal gravitation: F=GM1M2/R2 (G=6.67X10-11NM2/KG2, direction on their connection)3. Gravity and gravitational acceleration on celestial bodies: Gmm/r2=mg;g=gm/r2{r: Celestial Radius (M), M: Celestial Mass (kg)}4. Satellite bypass speed, angular velocity, period: v= (GM/R) 1/2;ω= (GM/R3) 1/2;t=2π (R3/GM) 1/2{m: center Celestial Mass}5. First (two or three) cosmic velocity v1= (g ground r Ground) 1/2= (gm/r) 1/2=7.9km/s;v2=11.2km/s;v3=16.7km/s6. Geostationary satellite gmm/(R-+h) 2=m4π2 (R-+h)/t2{h≈36000km,h: Height from the Earth's surface, R: The radius of the earth}Note:(1) The centripetal force required by celestial movement is provided by gravitation, and F to =F million;(2) The mass density of celestial bodies can be estimated by applying the law of gravitation;(3) The geostationary satellite can only run over the equator, and the operating cycle is the same as the Earth rotation period;(4) The orbital radius of satellites becomes small, the potential energy becomes smaller, the kinetic energy becomes larger, the speed becomes larger, the period becomes smaller (together three evils);(5) The maximum surrounding speed and the minimum transmitting speed of Earth satellites are 7.9km/s.
Three, force (common force, the synthesis and decomposition of force)
1) common forces
1. Gravity g=mg (direction vertical downward, g=9.8m/s*s≈10m/s*s, Action Point at center of gravity, suitable for near Earth surface) 2. Hooke's Law f=kx{direction along recovery direction, K: coefficient of stiffness (n/m), x: Deformation Amount (m)}3. Sliding friction f=μfn{the opposite direction of the object, μ: Friction factor, FN: Positive pressure (N)}4. Static friction 0≤f static ≤FM (opposite to the moving trend of the object, FM is the largest static friction)5. Gravitation F=gm1m2/r2 (G=6.67X10-11NM2/KG2, direction on their connection)Note:(1) the coefficient of stiffness k is determined by the spring itself;(2) The friction factor μ is independent of the size of the pressure and the size of the contact area, and is determined by the contact surface material characteristics and surface conditions;(3) FM slightly larger than ΜFN, generally regarded as fm≈μfn; 2) synthesis and decomposition of force
1. Synthesis of forces on the same line: F=F1+F2, Reverse: f=f1-f2 (F1>F2) 2. Synthesis of the angular force of each other:f= (f12+f22+2f1f2cosα) 1/2 (cosine theorem) F1⊥f2: f= (f12+f22)3. Resultant force size Range: | f1-f2|≤f≤| f1+f2|4. Orthogonal decomposition of forces: fx=fcosβ,fy=fsinβ (β is the angle between the resultant force and the x-axis tgβ=fy/fx)Note:(1) The synthesis and decomposition of force (vector) follows the parallelogram rule;(2) The relationship between force and separation is an equivalent substitution relationship, which can be used as a substitute for the joint action of force, and vice versa.(3) In addition to the formula method, can also be used to solve the drawing method, at this time to choose the scale, strict mapping;(4) When the value of F1 and F2 is certain, the greater the angle between F1 and F2 (α angle), the smaller the resultant force;(5) The synthesis of the force on the same line, can take the positive direction along the straight line, the direction of the force with the sign, the simplification is algebraic operation.
Iv. Dynamics (motion and force)
1. Newton's first Law of Motion (inertia): an object having inertia, always holding a uniform motion state or stationary state until an external force forces it to change this state.2. Newton's second Law of motion: F-=ma or a=f-/ma{is determined by the external force, in accordance with the direction of the external force}3. Newton's third Law of motion: f=-f′{minus indicates the opposite direction, F, f′ respectively acting on each other, the balance force and the Force Reaction forces difference, practical application: Recoil movement}4. The balance of the total force of f = 0, the promotion of the {orthogonal decomposition method, the principle of three-force sinks}5. Overweight: Fn>g, weightlessness: fn<g{acceleration direction downward, all weightlessness, acceleration direction upward, are overweight}6. The applicable conditions of Newton's Law of motion: suitable for solving the problem of low-speed motion [Color=rgb (!important)], suitable for macro objects, not for handling high-speed problems, not suitable for microscopic particlesNote: The balance state refers to the object being in a stationary or uniform linear state, or dumpers.
v. Vibrations and waves (transmission of mechanical vibrations and mechanical vibrations)
1. Simple Harmonic Vibration f=-kx{f: Recovery Force, K: Proportional factor, X: Displacement, minus sign F direction with x always reverse} 2. Simple pendulum cycle t=2π (l/g) 1/2{l: Pendulum Length (m), G: Local gravitational acceleration value, set conditions: Swing angle Θ<100;l>>r}
Six, impulse and momentum (the change of the force and momentum of the object)
1. Momentum: P=mv{p: Momentum (kg/s), M: Mass (kg), V: Speed (M/s), direction same as Speed}3. Impulse: I=ft{i: Impulse (Ns), F: Constant Force (N), T: Action time of force (s), direction determined by F}4. Momentum theorem: I=δp or ft=mvt–mvo{δp: Momentum change δp=mvt–mvo, vector type}5. Momentum: P before total =p or p=p ' can also be m1v1+m2v2=m1v1′+m2v2′6. Elastic collision: δp=0;δek=0{that the momentum and kinetic energy of the system are conserved}7. Inelastic collision Δp=0;0<δek<δekm{δek: Loss of kinetic energy, EKm: Maximum kinetic energy of loss}8. Completely inelastic collision δp=0;δek=δekm{to join together as a whole}9. The object m1 with V1 initial velocity and stationary object m2 elastic positive touch:v1′= (m1-m2) v1/(m1+m2) v2′=2m1v1/(m1+m2)10. Inference from 9--The exchange velocity (kinetic energy conservation, momentum conservation) when the equal mass elasticity is touching11. The Bullet m horizontal speed Vo into the static placed on the horizontal smooth ground of the long block M, and embedded in one of the mechanical energy Loss =mvo*vo/2-(m+m) vt*vt/2=fs relative {Vt: Common speed, F: Resistance, s relative to the bullet relative length of the bit of wood
Unity3d Essential Knowledge: a physics formula
