10.1 FundamentallawofdynamicsThis shows: the greater the mass, the stronger the ability to maintain its original motion state,namely the greater the mass, the greater the inertia. Therefore, mass is a measure of theinertia of a particle.In a gravitational field, all objects are subjected to the force of gravity. The acceleration of anobject in free fall under theforce of gravity is called the acceleration of gravity and isdenotedbyg.ItcomesfromthesecondlawGG=mgm =gWhere, G is the magnitude of the force of gravity on the object, which is called the weight ofthe object, and g is the magnitude of the acceleration of gravity. Usually take g = 9.8%,In the SI system of units, the units of length, mass, and time are the basic units, in meters,kilograms, and seconds. The units of force are derived units, newtons. That is:1(N) = 1(Kg)×1(m/ s2)
This shows: the greater the mass, the stronger the ability to maintain its original motion state, namely the greater the mass, the greater the inertia. Therefore, mass is a measure of the inertia of a particle. In a gravitational field, all objects are subjected to the force of gravity. The acceleration of an object in free fall under the force of gravity is called the acceleration of gravity and is denoted by . It comes from the second law G mg = g G m = Where, is the magnitude of the force of gravity on the object, which is called the weight of the object, and is the magnitude of the acceleration of gravity. Usually take . In the SI system of units, the units of length, mass, and time are the basic units, in meters, kilograms, and seconds. The units of force are derived units, newtons. That is: G g 9.8 2 s g = m 1( ) 1( ) 1( ) 2 N = Kg m s g 10.1 Fundamental law of dynamics
10.1FundamentallawofdynamicsItmustbeparticleedoutthattheforceonaparticlehasnothingtodowithcoordinates.butthe acceleration of a particle has something to do with the choice of coordinates, soNewton'sfirst and second laws donotapplytoany coordinates.The coordinate system inwhich Newton's laws apply is called the inertial coordinate system.Otherwise, it is noninertialcoordinatesystemThird Law (Law of Action and Reaction)The acting force and the reacting force between two bodies are always equal and oppositeacting on the two bodies simultaneously along the same action lineThetheoryofmechanicsformedonthebasisofNewton'slawsiscalledclassicalmechanics
It must be particleed out that the force on a particle has nothing to do with coordinates, but the acceleration of a particle has something to do with the choice of coordinates, so Newton's first and second laws do not apply to any coordinates. The coordinate system in which Newton's laws apply is called the inertial coordinate system. Otherwise, it is noninertial coordinate system. Third Law (Law of Action and Reaction) The acting force and the reacting force between two bodies are always equal and opposite, acting on the two bodies simultaneously along the same action line. The theory of mechanics formed on the basis of Newton's laws is called classical mechanics. 10.1 Fundamental law of dynamics
10.2Differentialequation of particlemotion1、 Differential equations of particle motion in vector formAccording to the basic equationof dynamicsma=Fd?rdiKinematics showsthat:adt?dtdv-YThen we can get:dFmormdt?dt2Differential equations of particle motionin rectangular coordinates2XFFTmmmxd?dt?2Zdt
1、Differential equations of particle motion in vector form According to the basic equation of dynamics: Kinematics shows that: ma F = 2 2 dt d r dt dv a = = Then we can get: F dt dv m = F dt d r m = 2 2 or 2、Differential equations of particle motion in rectangular coordinates 2 2 x d x m F dt = 2 2 y d y m F dt = 2 2 z d z m F dt = 10.2 Differential equation of particle motion
10.2Differentialeguationsofparticlemotion3,DifferentialeguationsofparticlemotioninnaturalcoordinatesdvVF=F0=F,mmdtp2.SC0=FFFmmor1dipThis is the differentialequation forthe motion of a particlein naturalcoordinates
3、Differential equations of particle motion in natural coordinates F dt dv m = Fn v m = 2 = Fb 0 or F dt d s m = 2 2 Fn s m = 2 = Fb 0 This is the differential equation for the motion of a particle in natural coordinates. 10.2 Differential equations of particle motion
10.3TwokindsofproblemsinparticledynamicsThe first type of problem: given the motion of a particle, find the force actingon it. The essence of this kind of problem boils down to a mathematical problemofderivation.The second kind of problem: given the force acting on the particle, to find themotion of the mass. The essence of this kind of problem can be reduced to solvingdifferential equation or integral problem in mathematics1、When the force is a constantor a simple functionofdv=F(t), so ("mdv= ['F(t)dt 。time,dt
The first type of problem: given the motion of a particle, find the force acting on it. The essence of this kind of problem boils down to a mathematical problem of derivation. The second kind of problem: given the force acting on the particle, to find the motion of the mass. The essence of this kind of problem can be reduced to solving differential equation or integral problem in mathematics. 1、When the force is a constant or a simple function of time, m F t dv ( ) ，so 。 dt = ( ) 0 0 v t v mdv F t dt = 10.3 Two kinds of problems in particle dynamics