User:Lavendar Vallery/sandbox/ISO 31-3 (expansion)

ISO 31-3 is the part of international standard ISO 31 that defines names and symbols for quantities and units related to mechanics. It is superseded by ISO 80000-4.

Its definitions include (note boldfaced symbols mean quantity is a vector):

Force
Force is needed to accelerate objects with mass and is defined in Newton's second law of motion which states that

$$\mathbf{F} = m\mathbf{a}$$

Moment of force, Torque
Torque is analogous to force in the context of rotation and is described by the formula using the cross product


 * $$\tau = \mathbf{r}\times \mathbf{F}\!$$

Linear momentum
Newton's second law of motion also relates to momentum with the following expressions:

$$\mathbf{p} = m\mathbf{v}$$

$$\mathbf{F} = \frac{\mathrm{d}\mathbf{p}}{\mathrm{d}t} $$

Photons also have momentum proportional to their energy.

$$\mathbf{p} = \frac{\mathbf{E}}{\mathrm{c}t} $$

(Linear) impulse
An impulse is described as force over time which is force integrated over time.

$$J = \int F \,\mathrm{d}t$$

Angular momentum
Angular momentum is analogous to linear momentum where angular velocity is used instead of linear velocity.

$$J = I \omega$$

where I represents inertia and replaces mass and $$\omega$$ is angular velocity instead of linear velocity.

Mechanical energy, Work
$$W = \int F \cdot \,\mathrm{d}s$$

Power

 * $$P =\frac{dW}{dt}$$

Pressure

 * $$p = \frac{F}{A}$$

Normal stress, Shear stress
...

#00031-3