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心智圖資源庫 Chapter 3 Momentum, Newton’s Law of Motion, Law of Conservation of Momentum
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Chapter 3 Momentum, Newton’s Law of Motion, Law of Conservation of Momentum
This is a mind map about Chapter 3 Momentum, Newton's Law of Motion, and Law of Conservation of Momentum. Includes the motion of rockets, application of Newton's laws of motion, inertial mass and momentum, etc.
編輯於2023-11-02 19:55:16
Chapter 3 Momentum, Newton’s Law of Motion, Law of Conservation of Momentum
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Chapter 3 Momentum, Newtonian Motion law, law of conservation of momentum
3.5 Dynamics in non-inertial frames
Inertial force in linear acceleration reference frame
In the non-inertial frame of linear motion, the inertial force F* on the particle is opposite to the acceleration a of the non-inertial frame, and is equal to the product of the mass m of the particle and the acceleration a of the non-inertial frame, that is
Manifestation: leaning forward and backward, overweight and weightlessness, tidal phenomena
Centrifugal inertia force (P77)
Condition: a non-inertial frame that rotates at a constant speed relative to the inertial frame
Kinetic equations:
Manifestation: apparent gravity, lost weight (South Africa bound for the equator)
Coriolis force
Condition: The particle moves relative to the rotating reference system
Kinetic equations:
Coriolis acceleration is not caused by the Coriolis force
Coriolis acceleration is observed in the inertial frame
The Coriolis force is observed in rotating, non-inertial frames
Reflection: Earth's rotation, northeast trade winds, typhoon formation, Falling to the east (Northern Hemisphere), washed by rivers
Coriolis force in the Northern Hemisphere: Looking along the direction of motion of an object, it always points to the right. The opposite is true for the Southern Hemisphere.
3.7 Momentum theorem of the particle system and the motion theorem of the center of mass
particle system momentum theorem
Particle system: A system composed of several interacting particles.
Internal force: the interaction force between the particles in the system
External force: the force exerted by other objects outside the system on any particle in the system
Only external forces contribute to the total momentum change of the system, Internal forces do not contribute to the total momentum change of the system. But internal forces play a role in the distribution of momentum within the system.
momentum theorem
Differential form:
Points form:
Newton's second law only applies to particles, The momentum theorem applies to both particles and systems of particles
Center of mass motion theorem
Centroid
There is a special point C in the particle system, let
In the Cartesian coordinate system, the coordinates of the center of mass are
The center of mass must be located on the line connecting m1 and m2, And the distance between the center of mass and each particle is inversely proportional to the mass of the particle
The position vector of the center of mass is related to the selection of the coordinate origin. However, the relative positions of the center of mass and each particle point of the system have nothing to do with the selection of the coordinate origin.
Center of mass motion theorem
The center of mass behaves the same as a mass point
The movement of the center of mass only depends on external forces, internal forces do not affect the movement of the center of mass
Application: fireworks, teapot falling, double stars, earth-moon system, sun-earth-moon system
The momentum of the particle system relative to the center of mass system
Center of mass coordinate system: with the center of mass as the origin, the coordinate axis is always parallel to the basic reference system
The momentum of the particle system relative to the center-of-mass coordinate system is always zero.
3.8 Law of Conservation of Momentum
Law of Conservation of Momentum of Particle System
condition
The system is not subject to external forces - an isolated system, momentum is conserved
The internal force of the system is impulse, and when the size of the external force is limited, External forces can often be ignored and the system momentum is conserved.
The law of conservation of momentum holds for all inertial systems, However, when solving specific problems, the momentum of each particle should be relative to the same inertial system.
Projection conservation of momentum along a certain coordinate axis
Momentum conservation can hold in a certain direction
3.9 Rocket motion
3.6 Momentum theorem expressed in terms of impulse
force impulse
The element impulse of the force within dt
The direction of element impulse and force are the same
The impulse of the force in the time interval t-t0
Direction: the direction of the vector sum of element impulses
average force
definition:
Impulse of mean force:
The direction of the total impulse is the same as the direction of the average force
Momentum theorem expressed in terms of impulse
Direction of impulse: direction of velocity increment
3.4 Application of Newton’s laws of motion
linear motion of particle
Linear motion under variable force
If the kinematic equation of the force is known, integral calculation is required
Kinetic equations:
Curvilinear motion of particle
Particle dynamics component formula
——Normal force (the algebraic sum of the projection of each force in the normal direction)
——Tangential force (the algebraic sum of the projection of each force in the tangential direction)
circular motion
balance of matter
Condition of particle equilibrium: When the particle is in equilibrium, the net force acting on the particle is equal to zero.
Particle equilibrium equation:
3.3 Active and passive forces
main force
gravity and weight
G=mg
Spring elastic force
F=kx
electrostatic field force
F=qE
Lorentz force
Passive force and binding force
tension in rope
Supporting force of supporting surface
Friction
3.2 Inertial mass and momentum
inertial mass
Mass is a measure of inertia
Operational definition of quality:
In classical mechanics, mass is a constant
In relativistic mechanics, mass increases with velocity, i.e.
Momentum, rate of change of momentum and force
momentum
Definition: The product of the mass of a particle and its velocity
When the force-receiving object is regarded as a particle, the force can be measured by the rate of change of the momentum of the force-receiving object.
The Momentum Theorem of a Point
The rate of change of the momentum of a particle with respect to time is equal to the vector sum of the forces acting on the particle
(Differential form of momentum theorem) It is the original form of Newton's law, which is also true in the theory of relativity.
Newton's laws of motion
Newton's second law
Scope of application: inertial reference system, particle and low-speed macroscopic objects
Newton's third law
The reference frame is not required to be an inertial frame
Newton's third law is actually the equivalent expression of momentum conservation in classical mechanics.
Galileo's principle of relativity
Any inertial reference system is equal or equal in the face of Newton's dynamic laws.
For describing the laws of mechanics, all inertial systems are equivalent
3.1 Newton’s first law and inertial reference system
Newton's first law: an isolated particle is at rest or moving in a straight line with uniform speed
inertial reference frame
A frame of reference relative to an isolated particle that is at rest or moving in a uniform straight line
A reference frame that moves in a straight line at a uniform speed relative to the inertial frame