MindMap Gallery Conservation law guide notes
The figure below introduces the relevant knowledge points of conservation laws, including the angular momentum theorem of particle points, the angular momentum theorem of particle groups, conservation laws and symmetry, problems with centered force fields, etc.
Edited at 2021-11-28 22:19:51This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
Angular momentum theorem and conservation law of particle group
Research: Spatial rotational effects of forces
Chapter framework
particle angular momentum theorem
particle angular momentum theorem
Establishment conditions:
It is established in the inertial frame. For the non-inertial frame, the moment of the inertial force is added.
For the definition of angular momentum and moment, there is moment and angular momentum for any reference point, but both must be for the same fixed reference point.
moment of force
The moment about an axis is the component representation of the moment about a point.
No matter which point on the axis is selected, the moment on the axis is the same
particle angular momentum
The angular momentum about an axis is the component representation of the angular momentum about a point
Conservation of particle angular momentum
Condition: The external moment in a certain direction is zero (angular momentum is a constant vector)
Angular momentum theorem and conservation law of particle group
The angular momentum theorem of particle groups
gravity moment
The moment of gravity on an object is equivalent to the moment of gravity when the mass is concentrated at the center of mass
The premise needs to be met: if the object is in a uniform gravity field
Couple moment
Forces that are equal in magnitude and opposite in direction and act on different particles are called force couples
Analogy to previous work: The work effect of a pair of internal forces has nothing to do with the selection of the reference system (for convenience of calculation, one of them is generally selected as the reference system)
If multiple forces choose different reference points, the sum of their moments will be different;
But if it is a pair of couple moments, the moment at any reference point is the same (it has nothing to do with the selection of the reference system, eg is relative to the center or both ends of the rod)
Law of conservation of angular momentum of particle group
Same as the case of a single particle
Typical example
If this question only considers cannonballs, the momentum of the system is not conserved.
Key to solving the problem:
Determination of conservation of angular momentum
Reasonable selection of reference points (convenient for calculation)
Angular Momentum Theorem of Particle System in Stationary System and Center of Mass System
The Angular Momentum Theorem of a Group of Particles in a Center-of-Mass System
Unit knowledge summary
Conservation laws and symmetry
From the perspective of the development of mechanical laws
There is a theorem first, and then there is conservation. Conservation is established under specific conditions.
theoretical level
There is a problem with the mental force field
three cosmic speeds
Effective potential energy and orbital characteristics
Task
Determining the orbital characteristics of stars based on system energy
Two-body monomer problem
Research object: Two bodies merge, the interaction force is in the direction of the connection, and there is no external force.
Routine treatment methods
Select the inertial frame and further discuss the motion of the two bodies.
Choose the center of mass system of the two, there is no external force, the center of mass system is the inertial system
Special handling measures
Use translational non-inertial mass center system
See the movement of one object from another object more intuitively
Use one of the objects as the reference system to further study the motion patterns of the other object
Final Results
By converting a two-body problem into a single-body problem, a series of physical rules and laws can be used