Wikibase - User contributions [en]

Classical mechanics

2026-09-24T15:13:07Z

Rongzhou: /* Gravity: any two mass attracts */

Classical mechanics is one framework to the study of [[mechanics]].

== Validity ==

== Vector description ==

Concise description of mechanical systems can be provided with [[vector]]s.

=== Reference frame ===

A reference frame is defined by an origin $O$, and the three unit vectors for each dimension of space: $\overrightarrow{x}$, $\overrightarrow{y}$, and $\overrightarrow{z}$.

It can be noted as:

$$R(O;\overrightarrow{x},\overrightarrow{y},\overrightarrow{z})$$

Conventionally, we choose unit vectors perpendicular to each other ($\overrightarrow{x}\bot\overrightarrow{y}\bot\overrightarrow{z}$), so each spatial direction is independent of another.

=== Objects in the reference frame ===

==== Motion: Position, velocity, accelaration ====

For an object (S) centered at point $P$, its '''position''' relative to reference frame $R$ can be described by its position vector $\overrightarrow{OP}=(\overrightarrow{x_P},\overrightarrow{y_P},\overrightarrow{z_P})$.

Then velocity, defined as the instantaneous change in position with respect to time, is then:

$$\overrightarrow{v_S}=\frac{d \overrightarrow{OP}}{dt}=(\overrightarrow{v_x},\overrightarrow{v_y},\overrightarrow{v_z})$$

Finally, acceleration, defined as the instantaneous change in velocity with respect to time, is then:

$$\overrightarrow{a_S}=\frac{d \overrightarrow{v_S}}{dt}=(\overrightarrow{a_x},\overrightarrow{a_y},\overrightarrow{a_z})$$

==== Mechanical contact: Force and moments ====

Any ''force'' $\overrightarrow{F}$ on object $(S)$ can be decomposed into component forces in each of the three independent spatial direction:

$$\overrightarrow{F}= \overrightarrow{F_x}+\overrightarrow{F_y}+\overrightarrow{F_z}$$

Therefore, it can be described as a vector:

$$\overrightarrow{F}= (F_x,F_y,F_z)$$

where $$F_x=\left\| \overrightarrow{F_x} \right\|$$ and so on.

As a result, if the force $\overrightarrow{F}$ is applied to point $A$ the ''moment'' $M(\overrightarrow{F}\to S)_B$ caused by such force at point $B$ is:

$$\overrightarrow{M}(\overrightarrow{F}\to S)_B=\overrightarrow{BA}\wedge \overrightarrow{F}$$

It can also be decomposed into components along three independent spatial directions:

$$\overrightarrow{M}=(M_x,M_y,M_z)$$

== Key principles ==

=== Newton's 1st law ===

Newton's 1st law describes the phenomenon '''inertia''': when the overall net external force is zero, the velocity of an object is maintained.<ref>{{#cite:Q1761}}</ref>

In vector notation, it can be written as:

{{#content:Q1766}}

The state that $\sum \overrightarrow{F}_{ext}=0$ is known '''mechanical equilibrium'''.

=== Newton's 2nd law ===

Newton's 2nd law describes the relationship between force, mass, and acceleration: the acceleration is proportional to force and the inverse of mass.<ref>{{#cite:Q1761}}</ref>

In vector notation, it can be written as:

{{#content:Q1767}}

=== Newton's 3rd law ===

Newton's 3rd law describes the reciprocity of force: when object $(S1)$ applies a force on object $(S2)$, $(S2)$ must apply a force opposite to $(S1)$ and equal in magnitude.<ref>{{#cite:Q1761}}</ref>

In vector notation, it can be written as:

{{#content:Q1768}}

=== Conservation of momentum ===

For any closed system, the momentum, defined as the product of mass and velocity (m\overrightarrow{v}), is conserved before and after any mechanical interaction within the system (including collision).<ref>{{#cite:Q1761}}</ref>

In vector notation, for a closed system of $n$ objects, the principle can be expressed as:

{{#content:Q1769}}

where $C$ is a constant.

Any change to momentum must be a direct result of an external force $\overrightarrow{F_{ext}}$ acting on a member of the system for a duration $t$. This change in momentum, known as ''impulse'', satisfies the following relationship:

{{#content:Q1770}}

=== Any motion carries kinetic energy ===

The kinetic energy of an object of mass $m$ and velocity $\overrightarrow{v}$ is:

{{#content:Q1771}}

Any change in kinetic energy, is the result of an external force acting over a given distance:<ref>{{#cite:Q1761}}</ref>

{{#content:Q1773}}

=== Conservation of energy ===

In a closed system, energy is conserved. It can be transformed from one form to another, but not created or destroyed:<ref>{{#cite:Q1761}}</ref>

{{#content:Q1772}}

=== Gravity: any two mass attracts ===

Two point masses at points $A$ and $B$ exerts a gravitational force on each other:<ref>{{#cite:Q1761}}</ref>

{{#content:Q1777}}

According to [[shell theorem]], spherically symmetric shapes can be approximated by point masses.

For real-world objects, whose shape may be irregular, if the distance between the object is much larger than the size of a given object ($\left\| \overrightarrow{AB} \right\|\gg R_A$), that object may be approximated as a point mass.

Otherwise, for arbitrary real-world objects:

{{#content:Q1778}}

{| class="wikitable"
! Symbol !! Meaning
|-
| $\mathbf r_A$ || position vector of an infinitesimal piece of body $A$.
|-
| $\mathbf r_B$ || position of an infinitesimal piece of body $B$.
|-
| $\rho_A(\mathbf r_A), \rho_B(\mathbf r_B)$ || density at those points.
|-
| $dV_A=dr_A^3, dV_B=dr_B^3$ || infinitesimal volumes.
|-
| $dm_A=\rho_A dV_A$, $dm_B=\rho_B dV_B$ || infinitesimal masses.
|-
| $\lvert \mathbf r_B-\mathbf r_A\rvert$ || distance between the two infinitesimal pieces.
|-
| $\dfrac{\mathbf r_B-\mathbf r_A}{\lvert \mathbf r_B-\mathbf r_A\rvert^3}$ || unit direction from $A$-piece to $B$-piece, divided by distance squared.
|}

The potential energy as a result of gravitational attraction is known as [[gravitational potential energy]].

<blockquote>
See also: [[Two body problem]]
</blockquote>

Two body problem

2026-09-24T15:04:13Z

Rongzhou: /* Classic form: planetary/satellite orbit (point mass approximation) */

In [[astronomy]], two body problems normally refer to the study of the gravitational interaction of two celestial objects.

== Classic form: planetary/satellite orbit (point mass approximation) ==

Approximate a star/planet as point mass $M$, and a planet/satellite orbiting around it as point mass $m$.

The orbit of the planet in the reference frame of the star satisfies the equation:

{{#content:Q1785}}

Where $\mu=G(M+m)$.

The orbit described by the equation is usually elliptical:

[[File:Two-body-problem.ggb]]

=== Derivation ===

Let

$$
\mathbf{r}=\mathbf{r}_m-\mathbf{r}_M
$$

be the vector from $M$ to $m$.

Let $r=|\mathbf{r}|$.

Gravity pulls $m$ toward $M$:

$$
m\ddot{\mathbf{r}}_m=-GMm\frac{\mathbf{r}}{r^3} \text{ (1)}
$$

Gravity pulls $M$ toward $m$:

$$
M\ddot{\mathbf{r}}_M=+GMm\frac{\mathbf{r}}{r^3} \text{ (2)}
$$

Therefore:

$$
\begin{cases}
\ddot{\mathbf{r}}_m=-GM\frac{\mathbf{r}}{r^3} \text{ (1)/m} \\
\ddot{\mathbf{r}}_M=+Gm\frac{\mathbf{r}}{r^3} \text{ (2)/M}
\end{cases}
$$

The relative acceleration of $m$ according to $M$, $\ddot{\mathbf{r}}$, is

$$
\ddot{\mathbf{r}}
=
\ddot{\mathbf{r}}_m-\ddot{\mathbf{r}}_M
$$

Substitute:

$$
\ddot{\mathbf{r}}
=
-GM\frac{\mathbf{r}}{r^3}
-
Gm\frac{\mathbf{r}}{r^3}
$$

$$
\boxed{
\ddot{\mathbf{r}}
=
-G(M+m)\frac{\mathbf{r}}{r^3}
}
$$

Usually, we note

$$
\boxed{
\mu=G(M+m)
}
$$

File:Two-body-problem.ggb

2026-09-24T15:01:52Z

Rongzhou:

== Licensing ==
[[Q320|CC BY-SA 4.0]]
== Attribution ==
Author: Rong Martin-Siebler ZHOU

Item:Q1786

2026-09-24T15:01:52Z

Rongzhou: Created the image item for Two-body-problem

Item:Q1786

2026-09-24T15:01:52Z

Rongzhou: Created the image item for Two-body-problem

Item:Q1786

2026-09-24T15:01:52Z

Rongzhou: Created the image item for Two-body-problem

Two body problem

2026-09-24T14:41:17Z

Rongzhou: Created page with "In astronomy, two body problems normally refer to the study of the gravitational interaction of two celestial objects. == Classic form: planetary/satellite orbit (point mass approximation) == Approximate a star/planet as point mass $M$, and a planet/satellite orbiting around it as point mass $m$. The orbit of the planet in the reference frame of the star satisfies the equation: {{#content:Q1785}} Where $\mu=G(M+m)$. === Derivation === Let $$ \mathbf{r}=\math..."

In [[astronomy]], two body problems normally refer to the study of the gravitational interaction of two celestial objects.

== Classic form: planetary/satellite orbit (point mass approximation) ==

Approximate a star/planet as point mass $M$, and a planet/satellite orbiting around it as point mass $m$.

The orbit of the planet in the reference frame of the star satisfies the equation:

{{#content:Q1785}}

Where $\mu=G(M+m)$.

=== Derivation ===

Let

$$
\mathbf{r}=\mathbf{r}_m-\mathbf{r}_M
$$

be the vector from $M$ to $m$.

Let $r=|\mathbf{r}|$.

Gravity pulls $m$ toward $M$:

$$
m\ddot{\mathbf{r}}_m=-GMm\frac{\mathbf{r}}{r^3} \text{ (1)}
$$

Gravity pulls $M$ toward $m$:

$$
M\ddot{\mathbf{r}}_M=+GMm\frac{\mathbf{r}}{r^3} \text{ (2)}
$$

Therefore:

$$
\begin{cases}
\ddot{\mathbf{r}}_m=-GM\frac{\mathbf{r}}{r^3} \text{ (1)/m} \\
\ddot{\mathbf{r}}_M=+Gm\frac{\mathbf{r}}{r^3} \text{ (2)/M}
\end{cases}
$$

The relative acceleration of $m$ according to $M$, $\ddot{\mathbf{r}}$, is

$$
\ddot{\mathbf{r}}
=
\ddot{\mathbf{r}}_m-\ddot{\mathbf{r}}_M
$$

Substitute:

$$
\ddot{\mathbf{r}}
=
-GM\frac{\mathbf{r}}{r^3}
-
Gm\frac{\mathbf{r}}{r^3}
$$

$$
\boxed{
\ddot{\mathbf{r}}
=
-G(M+m)\frac{\mathbf{r}}{r^3}
}
$$

Usually, we note

$$
\boxed{
\mu=G(M+m)
}
$$

Item:Q1785

2026-09-24T14:35:31Z

Rongzhou: Added content item: Planetary orbit

Item:Q1785

2026-09-24T14:35:31Z

Rongzhou: Added content item: Planetary orbit

Gravitational potential energy

2026-09-24T13:42:55Z

Rongzhou: Created page with "Gravitational potential energy, commonly noted $U$, refers to the energy incorporated in a system as a result of the gravitational attraction between its elements. == Zero reference point == Generally, we define the zero reference point: {{#content:Q1779}} Since there is no gravitational interaction when objects are at an infinite distance from each other. Then, the gravitational potential energy of a system measures the amount of work done by gravitational forces t..."

Gravitational potential energy, commonly noted $U$, refers to the energy incorporated in a system as a result of the gravitational attraction between its elements.

== Zero reference point ==

Generally, we define the zero reference point:

{{#content:Q1779}}

Since there is no gravitational interaction when objects are at an infinite distance from each other.

Then, the gravitational potential energy of a system measures the amount of work done by gravitational forces to move all masses of the system away from each other until the distance between them is infinite.

== Basic case: 2 point masses ==

For two point masses $m$, $M$, we can calculate the gravitational potential energy of the system mostly easily by constructing a cartesian coordinate system with one of the point masses, $M$, at the origin.

Then, if $m$ has position vector $ \mathbf r_1$:

$$\mathbf F_g(m)=-G\frac{Mm}{r_1^2}\hat{\mathbf r}_1$$

The potential energy of the system is:

$$U=-\int_{\infty}^{r_1}\left(-G\frac{Mm}{r^2}\right) \hat{\mathbf r} \cdot dr=-G\frac{Mm}{r}$$

<blockquote>
$$\hat{\mathbf r} \cdot dr = dr$$
</blockquote>

== Many point masses ==

Recall the gravitational potential energy between 2 point masses is

{{#content:Q1780}}

Applying the formula to all pairs of point masses in the system:

{{#content:Q1781}}

We can similarly derive a formula for the gravitational potential energy of a point mass external to the system:

{{#content:Q1782}}

== Continuous mass distribution ==

Any generic mass system can be modelled by a continuous mass distribution, with $\rho=0$ where there is no mass.

If the density at point with position vector $\mathbf{r}$ is $\rho(\mathbf{r})$:

{{#content:Q1783}}

<blockquote>
$dV=dr^3$: infinitesimal volume
</blockquote>

== Gravitational potential ==

If a test mass $m$ has gravitational potential energy $U(\mathbf{r})$ at a point, then the gravitational potential at that point is

$$\Phi(\mathbf{r})=\frac{U(\mathbf{r})}{m}$$

For another test mass $m_1$, the gravitational potential energy at the same point is then simply:

{{#content:Q1784}}

Item:Q1784

2026-09-24T13:40:52Z

Rongzhou: Added content item: Gravitational potential energy and gravitational potential

Item:Q1784

2026-09-24T13:40:52Z

Rongzhou: Added content item: Gravitational potential energy and gravitational potential

Classical mechanics

2026-09-24T13:34:58Z

Rongzhou: /* Gravity: any two mass attracts */

Item:Q1783

2026-09-24T13:22:00Z

Rongzhou: Added content item: Gravitational potential energy of continuous mass distribution

Item:Q1783

2026-09-24T13:22:00Z

Rongzhou: Added content item: Gravitational potential energy of continuous mass distribution

Item:Q1782

2026-09-24T13:12:53Z

Rongzhou: Added content item: Gravitational potential energy between a point mass and a system of many point masses

Item:Q1782

2026-09-24T13:12:53Z

Rongzhou: Added content item: Gravitational potential energy between a point mass and a system of many point masses

Item:Q1781

2026-09-24T12:59:17Z

Rongzhou: Added content item: Gravitational potential energy between many point masses

Item:Q1781

2026-09-24T12:59:17Z

Rongzhou: Added content item: Gravitational potential energy between many point masses

Item:Q1780

2026-09-24T12:54:09Z

Rongzhou: Added content item: Gravitational potential energy between two point masses

Item:Q1780

2026-09-24T12:54:09Z

Rongzhou: Added content item: Gravitational potential energy between two point masses

Item:Q1779

2026-09-24T12:37:27Z

Rongzhou: Added content item: Zero reference point for gravitational potential energy

Item:Q1779

2026-09-24T12:37:27Z

Rongzhou: Added content item: Zero reference point for gravitational potential energy

Classical mechanics

2026-09-23T12:48:26Z

Rongzhou:

Classical mechanics is one framework to the study of [[mechanics]].

== Validity ==

== Vector description ==

Concise description of mechanical systems can be provided with [[vector]]s.

=== Reference frame ===

A reference frame is defined by an origin $O$, and the three unit vectors for each dimension of space: $\overrightarrow{x}$, $\overrightarrow{y}$, and $\overrightarrow{z}$.

It can be noted as:

$$R(O;\overrightarrow{x},\overrightarrow{y},\overrightarrow{z})$$

Conventionally, we choose unit vectors perpendicular to each other ($\overrightarrow{x}\bot\overrightarrow{y}\bot\overrightarrow{z}$), so each spatial direction is independent of another.

=== Objects in the reference frame ===

==== Motion: Position, velocity, accelaration ====

For an object (S) centered at point $P$, its '''position''' relative to reference frame $R$ can be described by its position vector $\overrightarrow{OP}=(\overrightarrow{x_P},\overrightarrow{y_P},\overrightarrow{z_P})$.

Then velocity, defined as the instantaneous change in position with respect to time, is then:

$$\overrightarrow{v_S}=\frac{d \overrightarrow{OP}}{dt}=(\overrightarrow{v_x},\overrightarrow{v_y},\overrightarrow{v_z})$$

Finally, acceleration, defined as the instantaneous change in velocity with respect to time, is then:

$$\overrightarrow{a_S}=\frac{d \overrightarrow{v_S}}{dt}=(\overrightarrow{a_x},\overrightarrow{a_y},\overrightarrow{a_z})$$

==== Mechanical contact: Force and moments ====

Any ''force'' $\overrightarrow{F}$ on object $(S)$ can be decomposed into component forces in each of the three independent spatial direction:

$$\overrightarrow{F}= \overrightarrow{F_x}+\overrightarrow{F_y}+\overrightarrow{F_z}$$

Therefore, it can be described as a vector:

$$\overrightarrow{F}= (F_x,F_y,F_z)$$

where $$F_x=\left\| \overrightarrow{F_x} \right\|$$ and so on.

As a result, if the force $\overrightarrow{F}$ is applied to point $A$ the ''moment'' $M(\overrightarrow{F}\to S)_B$ caused by such force at point $B$ is:

$$\overrightarrow{M}(\overrightarrow{F}\to S)_B=\overrightarrow{BA}\wedge \overrightarrow{F}$$

It can also be decomposed into components along three independent spatial directions:

$$\overrightarrow{M}=(M_x,M_y,M_z)$$

== Key principles ==

=== Newton's 1st law ===

Newton's 1st law describes the phenomenon '''inertia''': when the overall net external force is zero, the velocity of an object is maintained.<ref>{{#cite:Q1761}}</ref>

In vector notation, it can be written as:

{{#content:Q1766}}

The state that $\sum \overrightarrow{F}_{ext}=0$ is known '''mechanical equilibrium'''.

=== Newton's 2nd law ===

Newton's 2nd law describes the relationship between force, mass, and acceleration: the acceleration is proportional to force and the inverse of mass.<ref>{{#cite:Q1761}}</ref>

In vector notation, it can be written as:

{{#content:Q1767}}

=== Newton's 3rd law ===

Newton's 3rd law describes the reciprocity of force: when object $(S1)$ applies a force on object $(S2)$, $(S2)$ must apply a force opposite to $(S1)$ and equal in magnitude.<ref>{{#cite:Q1761}}</ref>

In vector notation, it can be written as:

{{#content:Q1768}}

=== Conservation of momentum ===

For any closed system, the momentum, defined as the product of mass and velocity (m\overrightarrow{v}), is conserved before and after any mechanical interaction within the system (including collision).<ref>{{#cite:Q1761}}</ref>

In vector notation, for a closed system of $n$ objects, the principle can be expressed as:

{{#content:Q1769}}

where $C$ is a constant.

Any change to momentum must be a direct result of an external force $\overrightarrow{F_{ext}}$ acting on a member of the system for a duration $t$. This change in momentum, known as ''impulse'', satisfies the following relationship:

{{#content:Q1770}}

=== Any motion carries kinetic energy ===

The kinetic energy of an object of mass $m$ and velocity $\overrightarrow{v}$ is:

{{#content:Q1771}}

Any change in kinetic energy, is the result of an external force acting over a given distance:<ref>{{#cite:Q1761}}</ref>

{{#content:Q1773}}

=== Conservation of energy ===

In a closed system, energy is conserved. It can be transformed from one form to another, but not created or destroyed:<ref>{{#cite:Q1761}}</ref>

{{#content:Q1772}}

=== Gravity: any two mass attracts ===

Two point masses at points $A$ and $B$ exerts a gravitational force on each other:<ref>{{#cite:Q1761}}</ref>

{{#content:Q1777}}

According to [[shell theorem]], spherically symmetric shapes can be approximated by point masses.

For real-world objects, whose shape may be irregular, if the distance between the object is much larger than the size of a given object ($\left\| \overrightarrow{AB} \right\|\gg R_A$), that object may be approximated as a point mass.

Otherwise, for arbitrary real-world objects:

{{#content:Q1778}}

{| class="wikitable"
! Symbol !! Meaning
|-
| $\mathbf r_A$ || position of a tiny piece of body $A$.
|-
| $\mathbf r_B$ || position of a tiny piece of body $B$.
|-
| $\rho_A(\mathbf r_A), \rho_B(\mathbf r_B)$ || density at those points.
|-
| $dV_A, dV_B$ || tiny volumes.
|-
| $dm_A=\rho_A dV_A$, $dm_B=\rho_B dV_B$ || tiny masses.
|-
| $\lvert \mathbf r_B-\mathbf r_A\rvert$ || distance between the two tiny pieces.
|-
| $\dfrac{\mathbf r_B-\mathbf r_A}{\lvert \mathbf r_B-\mathbf r_A\rvert^3}$ || unit direction from $A$-piece to $B$-piece, divided by distance squared.
|}

User:Rongzhou/Nvim Regex

2026-09-23T07:06:31Z

Rongzhou: /* Katex */

== Markdown /md ==

Text <> list

<syntaxhighlight lang="text" copy>
:%s#^#- #
</syntaxhighlight>

<syntaxhighlight lang="text" copy>
:%s#^- ##
</syntaxhighlight>

== Katex ==

\[ $ <> $$ $ separator change:

<syntaxhighlight lang="text" copy>
:%s/\(\\(\(.\{-}$\\)\)\|$\\\[\(\_.\{-}$\\\]\)/\=submatch(1) != '' ? '$'.submatch(2).'$' : '$$'.submatch(4).'$$'/g
</syntaxhighlight>

<syntaxhighlight lang="text" copy>
:%s/\$\$$\_.\{-}$\$\$\|\$$.\{-}$\$/\=submatch(0) =~ '^\$\$' ? '\['.submatch(1).'\]' : '$'.submatch(2).'$'/g
</syntaxhighlight>

Classical mechanics

2026-09-23T06:47:23Z

Rongzhou: Created page with "Classical mechanics is one framework to the study of mechanics. == Validity == == Vector description == Concise description of mechanical systems can be provided with vectors. === Reference frame === A reference frame is defined by an origin $O$, and the three unit vectors for each dimension of space: $\overrightarrow{x}$, $\overrightarrow{y}$, and $\overrightarrow{z}$. It can be noted as: $$R(O;\overrightarrow{x},\overrightarrow{y},\overrightarrow{z})$$..."

Item:Q1778

2026-09-23T06:40:28Z

Rongzhou: Added content item: Gravitational force between two arbitrary objects (vector notation)

Item:Q1778

2026-09-23T06:40:28Z

Rongzhou: Added content item: Gravitational force between two arbitrary objects (vector notation)

Item:Q1777

2026-09-22T20:55:51Z

Rongzhou: Updated the item for Gravitational force between two point masses (vector notation) from Special:Update

Item:Q1777

2026-09-22T20:51:33Z

Rongzhou: Added content item: Gravitational force between two point masses (vector notation)

Item:Q1777

2026-09-22T20:51:33Z

Rongzhou: Added content item: Gravitational force between two point masses (vector notation)

User:Rongzhou/Nvim Regex

2026-09-22T20:42:33Z

Rongzhou: /* Markdown /md */

== Markdown /md ==

Text <> list

<syntaxhighlight lang="text" copy>
:%s#^#- #
</syntaxhighlight>

<syntaxhighlight lang="text" copy>
:%s#^- ##
</syntaxhighlight>

== Katex ==

\[ $ <> $$ $ separator change:

<syntaxhighlight lang="text" copy>
:%s/\\(\(.\{-}$\\)/$\1$/g
:%s/\\\[$.\{-}$\\\]/$$\1$$/g
</syntaxhighlight>

<syntaxhighlight lang="text" copy>
:%s/\$\$$.\{-}$\$\$/\\[\1\\]/g
:%s/\$$.\{-}$\$/\\$\1\\$/g
</syntaxhighlight>

Item:Q1773

2026-09-22T19:51:49Z

Rongzhou: Updated the item for Work and force (vector notation) from Special:Update

Item:Q1773

2026-09-22T19:51:16Z

Rongzhou: /* wbsetclaim-update:2||1 */ Property:P4: \\Delta E_k=\\int \\vec F_{ext} \\cdot d\\vec r

Item:Q1773

2026-09-22T19:49:47Z

Rongzhou: Added content item: Work and force (vector notation)

Item:Q1773

2026-09-22T19:49:47Z

Rongzhou: Added content item: Work and force (vector notation)

Item:Q1771

2026-09-22T19:42:40Z

Rongzhou: /* wbsetclaim-update:2||1 */ Property:P4: E_k=\\frac{1}{2}m \\left\\| \\overrightarrow{v} \\right\\|²

Item:Q1772

2026-09-22T19:38:38Z

Rongzhou: Added content item: Conservation of energy (vector notation)

Item:Q1772

2026-09-22T19:38:38Z

Rongzhou: Added content item: Conservation of energy (vector notation)

Item:Q1771

2026-09-22T19:37:53Z

Rongzhou: Added content item: Kinetic energy and velocity (vector notation)

Item:Q1771

2026-09-22T19:37:53Z

Rongzhou: Added content item: Kinetic energy and velocity (vector notation)

Item:Q1770

2026-09-22T16:46:42Z

Rongzhou: Added content item: impulse and force(vector notation)

Item:Q1770

2026-09-22T16:46:42Z

Rongzhou: Added content item: impulse and force(vector notation)

Item:Q1769

2026-09-22T16:40:30Z

Rongzhou: Added content item: Conservation of momentum (vector notation)

Item:Q1769

2026-09-22T16:40:30Z

Rongzhou: Added content item: Conservation of momentum (vector notation)

Item:Q1768

2026-09-22T16:32:12Z

Rongzhou: Added content item: Newton's 3rd law (vector notation)

Item:Q1768

2026-09-22T16:32:12Z

Rongzhou: Added content item: Newton's 3rd law (vector notation)

Item:Q1767

2026-09-22T16:29:13Z

Rongzhou: Added content item: Newton's 2nd law (vector notation)

Item:Q1767

2026-09-22T16:29:13Z

Rongzhou: Added content item: Newton's 2nd law (vector notation)

Item:Q1766

2026-09-22T15:32:01Z

Rongzhou: Added content item: Newton's 1st law (vector notation)