Rounding

Содержание и основные понятия

Even with the constant speed module, the circle is accelerated because the direction of the speed is constantly changing. The acceleration is directed to the center.
GEF · Grade 9
PIF · Baseline
Interactive model
period
frequency
angular speed
centrifugal acceleration
01
The physical picture
What happens and what boundaries the model has.
Main message
Even with the constant speed module, the circle is accelerated because the direction of the speed is constantly changing. The acceleration is directed to the center.
Centralism is not a separate force, but a role of equidistant real forces.
The period is the time of rotation, the frequency is the speed per second.
At a higher speed or a lower radius, a greater force is needed to the center.
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.
a
ц
=
v
2
R
a_{\mathrm{ц}}=\frac{v^2}{R}
a
c/
​
=
R
v
2
​
centrifugal acceleration
v
=
2
π
R
T
v=\frac{2\pi R}{T}
v
=
T
2
π
R
​
Linear speed
Review of the situation
On a horizontal turn, the centrifugal force of the car reports tyre friction on the road.
04
Links and application
In the real world
On a horizontal turn, the centrifugal force of the car reports tyre friction on the road.
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 theme "Cycle motion" through the model, not just the formula.
Outcome 2
Distinguish and correctly use terms: period, frequency, angular velocity.
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.
period
The time of one full repeat of oscillation or rotation.
frequency
Number of complete cycles per time.
angular speed
Production angle of rotation over time; characteristic of speed of rotation.
centrifugal acceleration
Corresponding to the centre of curvature, the circle acceleration v2/R.
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.
a
ц
=
v
2
R
a_{\mathrm{ц}}=\frac{v^2}{R}
a
c/
​
=
R
v
2
​
model effect
A centrifugal acceleration.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
∣
Δ
v
⃗
∣
v
≈
Δ
s
R
\frac{|\Delta\vec v|}{v}\approx\frac{\Delta s}{R}
v
∣Δ
v
∣
​
≈
R
Δ
s
​
In a short period, similar triangles of speed and radius give a ratio of speed to speed.
Δ
s
=
v
Δ
t
⇒
∣
Δ
v
⃗
∣
≈
v
2
Δ
t
R
\Delta s=v\Delta t\Rightarrow |\Delta\vec v|\approx\frac{v^2\Delta t}{R}
Δ
s
=
v
Δ
t
⇒
∣Δ
v
∣
≈
R
v
2
Δ
t
​
The doug is replaced by v Δt in a short time.
a
ц
=
lim
⁡
Δ
t
→
0
∣
Δ
v
⃗
∣
Δ
t
=
v
2
R
a_{\mathrm{ц}}=\lim_{\Delta t\to0}\frac{|\Delta\vec v|}{\Delta t}=\frac{v^2}{R}
a
c/
​
=
Δ
t
→
0
lim
​
Δ
t
∣Δ
v
∣
​
=
R
v
2
​
The acceleration limit is directed to the centre of the circle and has the specified module.
Conditions:
The instantaneous motion along the circle of the radius R; v is the relative speed and the formula sets the normal acceleration component.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
v
=
2
π
R
T
v=\frac{2\pi R}{T}
v
=
T
2
π
R
​
model effect
Linear speed.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
s
1
оборот
=
2
π
R
s_{1\,\text{оборот}}=2\pi R
s
1
turnover
​
=
2
π
R
In one full turn, the point passes the circle of the radius R.
t
1
оборот
=
T
t_{1\,\text{оборот}}=T
t
1
turnover
​
=
T
The period T is by definition equal to the time of one revolution.
v
=
s
t
=
2
π
R
T
v=\frac{s}{t}=\frac{2\pi R}{T}
v
=
t
s
​
=
T
2
π
R
​
When moving evenly, one turn is divided by its duration.
Conditions:
Equivalent movement along the circle of the radius R; T>0 and speed is understood as the instantaneous linear speed module.
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
The formula cannot be transferred to any situation simply because of the convergence of letters: the key condition of this topic is that the central force is not a separate force, but the role of an equal real force.
How to Check the Mind
The period is the revolution time, the frequency is the speed per second. Then check the units, the direction of the vectors, and the behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Rounding
Even with the constant speed module, the circle is accelerated because the direction of the speed is constantly changing. The acceleration is directed to the center.
Centralism is not a separate force, but a role of equidistant real forces.
The period is the time of rotation, the frequency is the speed per second.
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.