Review of this term1. Intro, Measurement, Estimating1.Units, Standards.2.Order of magnitude, rapid estimation,Scientific notation.3.Converting units1.Reference frames.2.Displacement, velocity, acceleration.3.Motion in 1 and 2 dimensions.4.Vector (i, j, k form).5.Projectile motion6.Circular motion7.Relative motion[]j v i v j t y i t x dtd dt r d v y x r r r r r r +=+== )()(Instantaneous velocity (瞬时速度) :Instantaneous Acceleration:22d d d d t r t v a r r r ==ja i a a y x r r r+=⎪⎪⎩⎪⎪⎨⎧====2222d d d d d d d d t y t v a t x t v a y y x x[]j v i v j t y i t x dtd dt r d v y x r r r r r r +=+== )()(Instantaneous velocity (瞬时速度) :Instantaneous Acceleration:22d d d d t r t v a r r r ==ja i a a y x r r r+=⎪⎪⎩⎪⎪⎨⎧====2222d d d d d d d d t y t v a t x t v a y y x xjv i v v y x ˆˆ+=r oxy0θ0v r vr gr xv 0ryv 0r(x 0, y 0)=x a xx v v 0=g a y −=gtv v y −=00()gt v j v i v −+=0000sin ˆcos ˆθθr 000000sin cos θθv v v v y x ==()()()20020200200sin 2sin cos gt gt v v gt v v v +−=−+=θθθr 0000cos sin tan θθθv gtv −=Velocity of projectile motionThe direction of velocity and acceleration.ωθr dtrd dt ds dt r d v =====r r θωˆr v =r Circular motiondtv d a rr =rr r rv r v rdtd v dt d v a ˆˆˆˆˆ22ωωθθ=====rO ’y ’Oyx ’xP''OO P O OP r r r r r r += Relative Displacement 相对位移Relative Velocity 相对速度()''''''OO P OO P O OO P O OP P v v dtr d dt r d dt r r d dt r d v r r rr r r r r +=+=+==Velocity in SVelocity in S’Velocity of S’relative to SSS’Relative motion1.Newton’s laws2.Mass, inertia.3.Application of Newton’s laws (in Mechanics and also in Electromagnetism)★4.Newton’s law of gravitation.22dt xd m ma F x x ==∑22dt yd m ma F y y ==∑22dt zd m ma F z z ==∑N IIka j a i a a z y x ˆˆˆ++=rChap. 4-6. Dynamics221r m m G F =Gravitational forcemg F =GravityOn the earth 2earth earth R mM G mg ≈Which is larger?1.Work.2.Work-Kinetic energy theorem.3.Conservative forces and nonconservative forces.4.Potential energy.5.Conservation of energy.and ,ˆˆˆk F j F i F F zy x ++=r .ˆˆˆk dz j dy i dx r d ++=r ∫∫∫∫∫++=++=⋅=fi f i f i z z z y y y x x x lz y x l dz F dy F dx F dz F dy F dx F r d F W )(r r Work done by a forceWork-Kinetic Energy Theorem 动能定理20221210mv mv mvdv dW W vv −===∫∫Net work done on an object equalsthe change of its kinetic energy.Conservative force保守力The work done by a conservative force on an objectmoving from one point to another depends only onthen initial and final position and is independent ofthe particular path.保守力对物体做的功仅决定于物体的始末位置而跟物体运动的路径无关。

e.g.: gravity (重力)，gravitational force (引力)，elasticforce (弹性力)，electromagnetic force (电磁力)。

The work done by a conservative force on an object moving any closed path is zero.沿任何闭合路径一周，保守力做功为0。

Nonconservative force非保守力The work done by a nonconservative force on anobject moving from one point to another depends not only on then initial and final position but also on the particular path.非保守力对物体做的功仅不仅决定于物体的始末位置而跟物体运动的实际路径有关。

e.g.: Friction (摩擦力)The work done by a nonconservative force on an object moving any closed path is zero.沿任何闭合路径一周，非保守力做功不为0。

Potential energy in general一般势能∫•−=−=ΔA B r d F A U B U U r r )()(independent of path和路径无关只和位置有关must be conservative 必须是保守力根据力计算势能变化的方法计算势能时积分下限取0势能位置。

This equation only gives the value of the change in potential energy. The exact value of potential energy depends on where U = 0.只能计算势能变化，势能的值依赖与0势能位置选取。

y U F xU F y x ∂∂−=∂∂−=,j F i F F y x r r r +=Known F is conservative or not?F 是不是保守力？保守力F 必须满足x F y F y x ∂∂=∂∂Principle of conservation of mechanical energy If the work done by nonconservative forces is zero, the mechanical energy of a system neither increases nor decreases. It stays constant----it is conserved.如果非保守力不做功或做功为0，系统的机械能守恒。

If only conservative forces are doing work, themechanical energy of a system neither increasesnor decreases. It stays constant----it is conserved.如果只有保守力做功，系统的机械能守恒。

(P174)Chap.9 Impulse and momentum1.Impulse and momentum2.Impulse-momentum theorem3.Average force4.Conservation of momentum5.CollisionThe linear momentum of a particle of mass m moving with a velocity is defined to be the product of the mass and velocity:vr vm p r r ≡∫=f it t dt F I r r Impulse 冲量Impulse-momentum theorem 动量定理The change in the momentum of a particle is equal to the impulse of the net force acting on the particle 粒子动量的变化等于作用在它上面的合力的冲量pI r r Δ=if t t i f t t p dt F t t F f i −Δ=−=∫r r r 1Average forceLaw of Conservation of momentum 动量守恒定律When the net external force on a system is zero, the total momentum conserves.不受外力的系统动量守恒。