Traffic relationship

Содержание и основные понятия

Coordinates and speed depend on the counting system. In classical mechanics, the speed of a body relative to one system is equal to the vector sum of its speed in a mobile system and the speed in the system itself.
GEF · 10 grade
PIF · Baseline
Interactive model
relativity
Mobile system
Transport rate
Time invariant
01
The physical picture
What happens and what boundaries the model has.
Main message
Coordinates and speed depend on the counting system. In classical mechanics, the speed of a body relative to one system is equal to the vector sum of its speed in a mobile system and the speed in the system itself.
The speed addition law is applied in an integral manner.
The trajectory of one body may vary from one system to another.
Classic addition is fair at speeds, many less speed of light.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
v
⃗
=
v
⃗
′
+
V
⃗
\vec v=\vec v^{\prime}+\vec V
v
=
v
′
+
V
Speed addition
r
⃗
=
r
⃗
′
+
R
⃗
\vec r=\vec r^{\prime}+\vec R
r
=
r
′
+
R
extension of radius-vectors
Review of the situation
The passenger is moving forward: for the earth, its speed is equal to the sum of the speed relative to the train and the speed of the train.
04
Links and application
In the real world
The passenger is moving forward: for the earth, its speed is equal to the sum of the speed relative to the train and the speed of the train.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Motor ratio" through the model, not just the formula.
Outcome 2
To distinguish and correctly use terms: relativity, mobile system, transport rate.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
relativity
Dependence of the traffic description and some measured values on the selected reporting system.
Mobile system
The counting system, moving relatively differently.
Transport rate
The speed of the mobile system is relative to the main system in the classical speed ratio.
Time invariant
The assumption of classical mechanics about the same time in all inertial counting systems.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
v
⃗
=
v
⃗
′
+
V
⃗
\vec v=\vec v^{\prime}+\vec V
v
=
v
′
+
V
model effect
Speed buildup.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
r
⃗
=
r
⃗
′
+
R
⃗
\vec r=\vec r^{\prime}+\vec R
r
=
r
′
+
R
The body radio is derived from its position in the mobile system and its starting position.
Δ
r
⃗
Δ
t
=
Δ
r
⃗
′
Δ
t
+
Δ
R
⃗
Δ
t
\frac{\Delta\vec r}{\Delta t}=\frac{\Delta\vec r^{\prime}}{\Delta t}+\frac{\Delta\vec R}{\Delta t}
Δ
t
Δ
r
​
=
Δ
t
Δ
r
′
​
+
Δ
t
Δ
R
​
The change in vector equality is divided into the Newtonian period.
v
⃗
=
v
⃗
′
+
V
⃗
\vec v=\vec v^{\prime}+\vec V
v
=
v
′
+
V
The relationship of change to time is the speed of the body and the mobile system.
Conditions:
The Galileos of the counting system are moving steadily; the speed is small compared to the speed of light, and the time is considered the same in both systems.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
r
⃗
=
r
⃗
′
+
R
⃗
\vec r=\vec r^{\prime}+\vec R
r
=
r
′
+
R
model effect
The addition of the radius vectors.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
O
T
→
=
O
O
′
→
+
O
′
T
→
\overrightarrow{OT}=\overrightarrow{OO^{\prime}}+\overrightarrow{O^{\prime}T}
OT
=
O
O
′
+
O
′
T
By the rule of moving vectors, the path from stationary start O to body T passes through the beginning of the O'mobile system.
R
⃗
=
O
O
′
→
,
r
⃗
′
=
O
′
T
→
\vec R=\overrightarrow{OO^{\prime}},\quad\vec r^{\prime}=\overrightarrow{O^{\prime}T}
R
=
O
O
′
,
r
′
=
O
′
T
The location of the movable beginning and the body relative to it shall be indicated.
r
⃗
=
r
⃗
′
+
R
⃗
\vec r=\vec r^{\prime}+\vec R
r
=
r
′
+
R
Geometric equality gives direct effect to the law of conversion of Galileo's coordinates in vector form.
Conditions:
Axes of systems are parallel and one system moves relatively slowly without rotation; radius vectors are taken at one point of Newton time.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
You can't put the formula on any situation just because it's a coincidence of letters. The key condition of this topic is that the Speed Adding Law is applied in a component way.
How to Check the Mind
The trajectory of the same body may vary from one system to another. Then check the unit, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Traffic relationship
Coordinates and speed depend on the counting system. In classical mechanics, the speed of a body relative to one system is equal to the vector sum of its speed in a mobile system and the speed in the system itself.
The speed addition law is applied in an integral manner.
The trajectory of one body may vary from one system to another.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.