A particle has mass but does not existVolume orshapePoint of, yesphysicsAn idealized model of.When the size and shape of the object do not work, or the role played is not significant and can be ignored, we approximately regard the object as aqualityAnd itsvolumeAn ideal object with negligible shape. The points with mass used to replace the object are called mass points (particles).
An object with a certain mass regardless of size.In fact, objects have a certain size, but if the size of an object is very small compared with the distance between it and other objects, or compared with the size of other objects, the object can be approximately regarded as a particle.For example, if the size of the planet is much smaller than the distance between the planets, the planet can be regarded as a particle - because the size is not included, the particle only considers the linear motion under the external force.
Since a particle has no size, many external forces acting on it can be combined into one force. On the other hand, the spin motion of a particle can be ignored when studying its motion.
Any object can be divided into many particles, and various complex motions of objects can be seen as the combination of many particle motions.Therefore, studying the motion of a particle is an introduction to mastering the various motions of various objects.Newton's second law is suitable for the motion law of a particle.This law, combined with Newton's third law, constitutes a means of studying objects of limited size.So "particle" is the simplest and most basic object to study the movement of objects.
A point with mass used to replace an object regardless of shape and size.It is an ideal model, which does not exist in fact.
In astronomy, a binary (multi star) celestial body moves around the same particle.(such as Pluto Kage, Earth Moon, extrasolar binary galaxy).
When studying the movement of the earth around the sun, the earth can be regarded as a particle, at this time, the size and shape of the earth have no obvious influence on the problems considered;When studying the earth and its satellites, the earth cannot be regarded as a particle, because the size and shape of the earth at this time have a significant impact on the problems studied.
Judgement theorem
Announce
edit
To regard an object as a particle, it depends on thenature, independent of the object itself.So,Can objects be regarded as particlesOne of these needs to be met:
When the size of the object is extremely small compared with other distances in the problem under study.
The motion of all parts of an object is the same, and the motion of any point can represent the motion of the whole object.
Under ideal conditions, the following conditions are met:
(1) The motion of all points on the object is the same, so it can be regarded as a particle.
(2) The size and shape of the object have little influence on the research problem, so it can be regarded as a particle.
(3) A rotating object can also be regarded as a particle as long as its rotation is not studied and complies with Article 2.
A moving object regarded as a particleThere are the followingtwo typessituation:
(1) The shape and size of moving objects are negligible compared with the problems it studies, such asrevolutionThe earth can be regarded as a particle.
(2) DotranslationSince the motion of each point on the object is the same, one point can represent the motion of the whole object.
explicate
Announce
edit
A particle has mass but does not existvolumePoint with shape.Generally, if the size of the object is relatively small or has little impact on the research object, the object can be regarded as a particle.
Mass point,physicsProper nouns.When the shape and size of the object itself are not considered, and the mass is regarded as concentrated at a point, the object is regarded as a "particle".When studying problems, use particles instead of objects, and do not consider the space between the points on the objectmotion state Differences.It is the process of mechanicsScientific abstractionThe concept obtained is aideal model 。The object that can be regarded as a particle is often not very small, so it cannot be compared withMicroparticleSuch as electronicsconfuseGet up.If the problem studied does not involve rotation or the size of the object is very small compared with the distance involved in the problem, the actual object can be abstracted as a particle.For example, in the studyEarth revolutionWhen,Earth radiusIt is much smaller than the distance between the sun and the earth, so the earth can be regarded as a particleearth rotationWe should not regard it as a particle.Another example is that the object istranslationWhen the motion of the interior is the same everywhere, it can be regarded as a particle.Therefore, whether an object is regarded as a particle or not depends entirely on the nature of the problem studied.
A particle is a geometric point obtained by simplifying an object, which has only mass but no size or shapeclassical mechanicsThe most basic model commonly used in.Move horizontally (seemechanical movement）The displacement, velocity and acceleration of any point in the body are the same regardless of its size and shapecentroidThe motion of this point can be summarized as the motion of a particle.
In the earth's revolution around the sun, any point in the ball is opposite to the sundisplacement, speed and acceleration are slightly different, but the radius of the earth is far less than the distance between the earth and the sun, and the above differences are also far less than the geocentricdisplacement, speed and acceleration, which can be ignored, can still be seen as the revolution of particles.In the rotation of objects, such as the rotation of the earth, there is a huge difference in the direction and magnitude of the displacement, velocity and acceleration of each point in the ball, which cannot be ignored at all, so it cannot be regarded as a particle.But it can divide the object into infinitesimalPrime elementEach particle can be regarded as a particle, and the rotation of the object becomes the sum of the motions of infinite particles, that isParticle systemThe movement of.
On the other hand, from the point of view of the gravity of an object, if the size of the object is far smaller than the distance between it and another object that generates the gravitational field, its shape and size can be ignored and it can be regarded as a particle;When they are close, they must be regarded as particle systems.Therefore, the mechanical motion of all objects in the world can be regarded as the motion of particles or particle systems, and particle kinematics and particle system dynamics have become the basis of classical mechanics.
If the mass of a particle is M1, it is located at the point P1 on the axis, and the coordinate of P1 is X1;The mass of a particle is M2, which is located at point P2 on the axis, and the coordinate of P 2 is X2, so the coordinate X of the center of gravity P of the particle system formed by these two particles=(M1X1+M2X2)/(M1+M2)
If you just want to describe the motion characteristics of an object (how to change its own state will not affect the movement of the external movement), you can use it as a particle
This is a metaphor:
The Earth can be used as a particle
If there is a train going from XiamenBeijingWords of
It can be used as a particle on the map (even if the train is round or square, it has no effect on what you want to describe)
When you want to describe the movement of this train when it completely passes 100 meters, you can't regard it as a particleBecause it has the length of the body, and this length will change its motion characteristics (including the rear of the car, for example), so it cannot be regarded as a particle.
If you want to study a ball that rotates in place, it cannot be regarded as a particle, because if it is regarded as a particle, its rotation cannot be explored
Relevant instructions
Announce
edit
1. Particle is an idealized model, which is the scientific abstraction of actual objects under certain conditions.
2. A particle is not necessarily a very small object. As long as the shape and size of the object are irrelevant or secondary factors in the problem under study, that is, the shape and size of the object have a small impact on the problem under study, the object can be regarded as a particle.It focuses on the influence of objects on the system when studying motion and force, ignoring some complex but unrelated factors.
1. It only occupies position, not space, that is, it is one-dimensional
2. It has the total mass of the object it replaces.
Movement
Announce
edit
Kinematic equation
In a selected reference system, when a particle moves, its position P (x, y, z) changes at any time according to a certain rule, so the position is tfunction, this function can be expressed as:
x=x(t) ,y=y(t),z=z(t)
They are called kinematic equations of particles.
Geovector
stayCoordinate systemIn, the position vector commonly used for the position of the particle is from the origin to the position of the pointDirected line segment, denoted by vector r.[1]
Particle group
Announce
edit
definition
The mechanical system composed of many particles interacting with each other is calledParticle group, also calledParticle system。
nature
1. Particle groups must have each otherInteraction。(A group of unrelated mosquitoes and flies as well as scattered sand are not particle groups)
2. Between particle groupsinternal forceAndexternal force: The internal force is recorded as F (i), and the external force is recorded as F (e).Property: The vector sum of internal forces in the particle group is always zero.
3. Momentum theorem and conservation law of particle group: it is one of the foundations of rigid body mechanics.
Theorem of momentum of a group of particles The rate of change of momentum of a group of particles is equal to the vector sum of external forces on the group of particles.
twoTheorem of center of mass motionThe product of the mass of the particle system and the acceleration of the center of mass is always equal to the vector sum of all external forces on the particle system.
The momentum conservation law of three particle group If the sum of the external force vectors of the particle group is zero, then the momentum of the particle group P=constant.
The law of conservation of momentum of particle group shows that if ∑ Fi (e)=0, then P=Pc=constant, that is, the center of mass moves in a uniform straight line (Vc=constant), and the internal force will not cause the change of the center of mass motion state.
4. Momentum theorem of particle group and conservation law of moment of momentum
Theorem of fixed moment of momentum of a group of particles to fixed point O.The time change rate of the momentum moment of the particle group to the fixed point is equal to the external torque.
Theorem of Momentum of Momentum of Two Pairs of Masses: 1. The coordinate system of the center of mass is assumed to be a static system. If another coordinate system cx'y'z 'moves with the motion of the group of particles, the origin is taken from the center of mass of the group of particles, and the coordinate axis is parallel to the coordinate axis of the basic system oxyz, then cx'y'z' is called the center of mass coordinate systemThe characteristics of the centroid coordinate system are: in the centroid system, the position vector of the centroid rc=0
2. The momentum moment theorem dJ '/dt=M' for the center of mass system shows that the rate of change of the momentum moment J 'for the center of mass to time is equal to the torque of the external force acting on the group of particles to the center of mass (this formula is called the momentum moment theorem for the center of mass).This formula also shows the particularity of the center of mass system: in general, the center of mass system is not an inertial system, but the theorem of the moment of momentum of the group of particles in the center of mass system remains the same form as that in the inertial system.This formula also shows that the moment of inertia force and internal force to the center of mass is always zero.
3. Kinetic energy theorem of particle group and conservation law of mechanical energy
The change of kinetic energy of a group of particles is equal to the sum of work done by external forces and internal forces on the group of particles (kinetic energy theorem).Obviously: only when the distance between two particles remains unchanged (such as a rigid body) when moving, the work done by internal force will be zero.Generally, the work done by internal force is not zero.Special case: if the external force and internal force are both conservative forces, the mechanical energy of the particle group is conserved.
Two pairs of kinetic energy theorem of the center of mass The change of kinetic energy of a group of particles on the center of mass system is equal to the sum of work done by external forces and internal forces on the center of mass system.
threeKonig's theorem : The total kinetic energy of the particle system is equal to the kinetic energy of the center of mass when all the masses are concentrated at the center of mass, plus the kinetic energy of each particle relative to the translational coordinate system of the center of mass.
Defect defined by particle
Announce
edit
The definition of particle is the earliest scientific definition of classical physics, which only considers the mass of the object without considering the internal charge of the object, so that the classical mechanical system based on the definition of particle cannot be fully compatible with electromagnetism, electrodynamics, special relativity and modern physics.
Modern physics proves that the final material composition of any object is three basic particles: electron (with unit negative charge), proton (containing two u-quarks with 2/3 charge and one d-quark with - 1/3 charge) and neutron (containing two d-quarks and one u-quark)[2]。Although the atoms, molecules or objects composed of them are mostly electrically neutral, their internal charge composition cannot be ignored.
For example, when studying the moving hydrogen atom, if the hydrogen atom is abstracted as a particle, it can only be connected with classical mechanics.If we regard it as the movement of electrons around the atomic nucleus, it is related to electromagnetism, electrodynamics, atomic physics, and quantum mechanics[3]。
