**Work** and **power** of the force $\vec{F}$: $$W = \int \vec{F}.d\vec{r} = \int F_s ds, P = \vec{F}.\vec{v}$$

Increment of the **kinetic energy** of a particle: $$T_2 - T_1 = W,$$ where $W$ is the **work** performed by the resultant of *all* the forces acting on the particle.

**Work**performed by the forces of a field is equal to the decrease of the**potential energy**of a particle in the given field: $$ W = U_1 - U_2.$$- Relationship between the
**force**of a field and the**potential energy**of a particle in the field: $$\vec{F} = -\vec{\nabla} U,$$*i.e.*the force is equal to the anti-gradient of the potential energy. - Increment of the
**total mechanical energy**of a**particle**in a given potential field: $$ E_2 - E_1 = W_{extr},$$ where $W_{extr}$ is the algebraic sum of works performed by all*extraneous*forces, that is, by the forces not belonging to those of the*given*field. - Increment of the
**total mechanica**l energy of a**system**: $$E_2 - E_1 = W_{ext} + W_{int}^{noncons},$$ where $E = T + U$, and $U$ is the*inherent*potential energy of the system. - Law of
**momentum variation**of a system: $$\frac{d\vec{p}}{dt} = \vec{F},$$ where $\vec{F}$ is the resultant os all*external*forces. **Equation of motion**of the system's**center of inertia**: $$m \frac{d \vec{v_C}}{dt} = \vec{F},$$ where $\vec{F}$ is the resultant os all*external*forces.**Kinetic energy**of a system:$$T = \widetilde{T} + \frac{m v_C^2}{2},$$ where $\widetilde{T}$ is its kinetic energy in the system of center of intertia.- Equation of dynamics of a
**body with variable mass**: $$m \frac{d \vec{v}}{dt} = \vec{F} + \frac{d m}{dt} \vec{u},$$ where $\vec{u}$ is the velocity of the separated (gained) substance relative to the body considered. - Law of
**angular momentum variation**of a system: $$\frac{d\vec{L}}{dt} = \vec{\tau},$$ where $\vec{L}$ is the angular momentum of the system, and $\vec{\tau}$ is the total**moment**of all*external*forces. **Angular momentum**of a system: $$\vec{L} = \widetilde{\vec{L}} + \vec{r_C}\times\vec{p},$$ where $\widetilde{\vec{L}}$ is its angular momentum in the system of the**center of inertia**, $\vec{r_C}$ is the radius vector of the center of inertia, and $\vec{p}$ is the momentum of the system.

### Exclude node summary :

n

### Exclude node links:

0