大学物理总结1

2020-03-04 01:10:44 来源：范文大全收藏下载本文

Mechanics

Kinematics for particles

1、equation of motion and path equation (1)equation of motion

 (a)vector form：r(t)x(t)iy(t)jz(t)k

(b)components form：xx(t)，yy(t)，zz(t)

(2) path equation f(x,y,z)=0 (cancel out time t)

2、Quantities of describing motion

(1) derivationderivationvarintergrationintergration

Hints: (a) train rule

advdvdxdvvf(x)dtdxdtdx

(b) initial conditions

v(2)

position vector

r(t)x(t)iy(t)jz(t)k

displacement

rr2r1xiyjyk

drdxdydzvijkvivjvkvelocity

xyz dtdtdtdtv.0,vx.0,vt.0

acceleration

a.rectangular coordinate system 222dvdvxdvydvzdxdydzaijk2i2j2kaxiayjazkdtdtdtdtdtdtdt

b.natural coordinate system dvv2aatanatannndt

3、Projectile motion (1) characteristic:

agj

Uniformly accelerated motion (2) .motion equation

a.component form

xv0cos t1yv0sin tgt22

b.vector form

1212rv0tgt(v0cosiv0sinj)tgtj22

4、circular motion (1) angular variables

（angular coordinate）

（angular displacement）

ddt (angular velocity)

dd22(angular acceleration) dtdt

(2) relation between linear and angular variables sR,

vR

2aRn

(normal acceleration)

atR

(tangential acceleration)

5、Relative motion rr

212r1 vv

212v1

rposition transform

13r1r3r1r2r2r3r12r2

3 vvvvelocity transform

131223

aaaacceleration transform

131223

Dynamics for particles 1.Newton’s laws of motion

(1).Newton’s first law of motion (law of inertia) F0, a0

Every body continues in its state of rest or of uniform speed in a straight line as long as no net force acts on it.(2)． Newton’s second law of motion dpFmadt

The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its ma.The direction of the acceleration is the direction of the net force acting on the object.

(3)．Newton’s third law of motion F12F

21Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first. 2.common forces (1) elastic force:

Fkx(restoring force)

k: spring constant， (2) frictional force Ffr a.kinetic friction FfrFk Nb.static friction

0FfrFf(rmax)Fs

N(3) Gravitation:

FGm1m2 ,r2G6.671011Nm2kg2 Gravitational constant (4) Weight

FGmg

Application of Newton’s laws

a) Draw a free-body diagram for every object whose motion is to be analyzed.

b) Label all forces acting on the objects.c) Choose a coordinate system for each object under consideration d) Apply Newton’s second law in component form.

e) Additional geometric and other constrains may need to be considered in some cases in order to have enough equations.f) Algebraically solve for the unknowns first, then substitute numbers to obtain quantitative answers.This allows you to check your work more easily and reduces errors in calculations.g) Algebraically solve for the unknowns first, then substitute numbers to obtain quantitative answers.This allows you to check your work more easily and reduces errors in calculations.3.work and energy (1).

work

WabFdl

dWFv

power Pdt(2) Conservative force：Work done by the force depends only on the initial and final positions.

(3).potential energy aWFdl0l

\"0\"UaFdl,

“0” represents zero potential energy.

Weight potential energy

Umg h

Gravitational potential energy U12GMm

rElastic potential energy

Ukx2

4 .The work-energy principle and conservation of mechanical energy (1) The work-energy principle WnetK

for one particle WinWexK2K1K

for system of particles The net work done on an object (system) is equal to the change in its kinetic energy (2) The work-energy principle

WexWincE2E1

(3) Principle of conservation of mechanical energy WeWinc0 , E2E1constant If only conservative forces are doing work, the total mechanical energy of a system is conserved.

5、linear momentum and its conservation

t2(1).impulse:

JFdt

t1(2).impulse theorem t2JFdtP

(for particle)

t1t（for system of particles） JFextotaldtP2P1P2t1The change in momentum of an object is equal to the impulse acting on it. (3) The law of conservation of linear momentum

if Fext0, P=constant

When the net external force on a system is zero, the total momentum remains constant.6 .Center of ma (CM)

(1) position of CM ：rcmirii1n

(discrete particles)

M1

rcM

(continuous body) rdm（2） Newton’s second law for CM

dvcFextMacMdt

The sum of all the forces acting on the system is equal to the total ma of the system times acceleration of its center of ma.7.Collisions The momentum can be considered to be conservative （1）Conservation of kinetic energy (perfect) elastic collision

Conservation of momentum and kinetic energy （2）Lose kinetic energy

Inelastic collision

Completely inelastic collision: the lo of energy is a maximum.（3）Gain kinetic energy

superelastic collision