Chapter1 kinematics

1.displacement：Δx=x-x0

2.speed-velocity

（1）speed=d/t

（2）v=dx/dt

3.acceleration

（1）a=dv/dt

（2）constant acceleration

①x=x0+1/2（v+v0）t=x0+v0t+1/2 at*2

②v=v0+at

③v*2-v0*2=2aΔx

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Chapter2 dynamics

1ΣF=ma,ΣF means net external force

N=kg m s*（-2）

2 gravitational force

F=GMm r*（-2），GM=gR*2

3 overweight weightless

Fn(support force)=mg+ma

（1）Fn is the reading of the scale, and mg is actually the weight.

（2）when the a＞0，Fn＞mg，overweight，and weightless the opposite

4 static and kinetic frictional force

（1）fs≤fs（max）=μsFn (actually the maximum of static frictional force is larger than constant kinetic frictional force )

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Chapter 3 Work and energy

1 W=Fs=|F||S|cosα

2 kinetic energy（動能）

（1）Ek=1/2 mv*2

(2) the work done by net external force equal to the change of the kinetic energy:

W=Ekf-Ek0

3 gravitational potential energy(重力勢能)

Wg=mg(h0-hf)=-mgΔh

Ep（g）=mgΔh

4 elastic potential energy（彈性勢能）

Ep（tension）=1/2k（Δx）*2

5 mechanical energy

(1)Emc=Ek+Ep

(2)Wnc=ΔEk+ΔEp

① the force external to the system leads to the change of the mechanical energy, and calculate by the change of kinetic energy and the potential energy. That is to say, we can use the mechanical energy to solve the problem in a system

②compare to the constancy in mechanical energy， theorem of kinetic energy is to solve the problem in an object. For instance, if you work out the net force on an object and the relative distance, you can calculate the total work and thus know the change of the kinetic energy.

6 Power（功率）

P=W/t

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Chapter 4 Impulse and momentum

1 impulse：J=（ΣF）Δt

2momentum：p=mv

3（ΣF）Δt=m（vf-v0）

（1）the change of momentum can be calculated by impulse

（2）if the net external force is zero，the momentum will be constant

4collision

（1）elastic one：ΔEk=0，but momentum remains the same

(2)inelastic one:ΔEk≠0 ，and stick together while completely inelastic

5center

（1）Xcm=Σ（i=1，n）mixi/Σ（i=1，n）mi

（2）Vcm=Σ（i=1，n）mivi/Σ（i=1，n）mi

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Chapter 5 uniform circular motion

1translational to rotational

(1) x=x0+v0t+1/2at*2，θ=θ0+ω0t+1/2αt*2；x=rθ

(2)v，ω；v=rω

(3)a=dx/dt，α（角加速度）=dθ/dt

(4)v=v0+at，ω=ω0+αt，v=rω

(5)m,I=mr*2

(6)F=ma, ┏=Fxr，

(7)Ek=1/2mv*2,Ek’=1/2Iw*2

(8)W=Fx=┏θ

(9)dim clockwise as negative direction

2.θ=Δv/v=vΔt/r---Δv/Δt=v*2/r=ac

3.v=2Πr/T=rω

4.acceleration

（1）ac=v*2/r=rω*2，direction：to the center

（2）aT=rα=r dω/dt，direction： tangential（切向）

5. ┏=Fxr=Iα

（1）|┏|=|F||r|sinθ

（2）positive direction： counter clockwise

6.I

(1) one point:I=mr*2

（2）x points：I=Σmiri*2

（3）ring：

①I=mr*2

②

（4）rod

①I=1/3mL*2

②I=1/12mL*2

（5）plate round：I=1/2Mr*2

（6）ball：I=2/5mR*2

（7）I=Ic+md*2

①ball on the ground：（1+2/5）mR*2

②ring（實心）：（1+1/2）mR*2

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7.W=┏θ

8.Ek=1/2Iω*2

9.L（angular momentum，角動量）=Iω

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Chapter 6 Simple Harmonic Motion,elasticity

Ⅰideal spring：F=-kx

1.x=Acosωt，ω=2Πf=2Π（T*-1）

2.v=Aωcosωt, a=Aω*2 cosωt

3.F=kx=ma（x）

（1）-kAcosωt=-mAω*2cosωt

(2) ω=(k/m)*0.5

4.energy: Ep=1/2kx*2

Ⅱmodel of pendulum

1.（1）Σ┏=Fx=-mgLsinθ=-mgLθ

（2）θ=Acos cosωt/L

（3）Σ┏=-mgLcosωt

2.（1） Σ┏=Iα

（2）α=a/L=-ω*2Acosωt/L

（3）combine together：ω=（mgL/I）*0.5

Ⅲtwo other models

1.F=Y（ΔL/L0）A

2.F=S（Δx/L0）A

Chapter7 fluid

1.Δp=ρhg，F=ρgV

2.pascal‘s principle（F proportional to Area）

（1）F1/F2=S1/S2

（2）A1h1=A2h2

3.continuity（流量）

Δm=ρV=ρAvΔt

(1)Δm/Δt=ρVA

(2)ΔV/Δt=Q=Av

4.equation of Bernoulli

P1+1/2ρv1*2+ρgy1= P2+1/2ρv2*2+ρgy2

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Chapter8 Temperature and heat

1.Tc=5/9（Tf-32），T=Tc+273.15

2.liner thermal expansion（熱脹冷縮）

（1）ΔL=αL0ΔT

（2）ΔV=βL0ΔT

3.Q

(1)Q=cmΔT

（2）Q=mL（it means that if water（solid，0） turns into liquid，0，how much heat it needs

4.three ways of heat transference

（1）convection（對流）Q=kAΔTt/L

（2）conduction（熱傳遞）Q=cmΔT=mL

（3）radiation（輻射）Q= ξeAtT*4，其中ξ=5.67x10*（-8）J/（sm*2K*4）

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Chapter9 waves and sound

1 conception

(1)A, λ，T，f

（2）f=1/T，v=λ/T=λf

2 speed of sound：v=（γkT/m）*0.5

3 sound intensity：I

(1)I=P/A

(2)in a sphere：A=4Πr*2

（3）①Io=10*-12 W/m*2

②I=1 W/m*2

（4）dB：β=10ln（I/Io），Io=10*-12 W/m*2

4 doppler effect

fo=fs（v±vo）/（v-+vs）

（1）upper：if observer moves to source，+

（2）lower： if source moves to observer，-

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