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 It is superseded by ISO 80000-4.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):

Quantity		Unit			Remarks
Name	Symbol	Name	Symbol	Definition
Force	F	newton	N	1 N = 1 kg·m/s2	Unit named after Isaac Newton
Moment of force, Torque	M, ${\boldsymbol {\tau }}$		N·m	1 N·m = 1 kg·m2/s2	The unit is dimensionally equivalent to the units of energy, the joule; but the joule should not be used as an alternative for the newton metre.
Linear momentum	p		kg·m/s or N·s
(Linear) impulse	J		N·s or kg·m/s
Angular momentum	L		kg·m2/s or N·m·s
Mechanical energy, Work	E, W	joule	J	1 J = 1 kg·m2/s2 = 1 Pa·m3 = 1 W·s	Unit named after James Joule. The joule is dimensionally equivalent to the units of torque and moment of force but should be used in preference to the newton metre (N·m).
Power	P	watt	W	1 W = 1 J/s = 1 N·m/s = 1 kg·m2/s3	Unit named after James Watt.
Pressure	p	pascal	Pa	1 Pa = 1 N / m2 = 1 kg/(m·s2)	Named after Blaise Pascal.
Normal stress, Shear stress	$\sigma ,\tau$	pascal	Pa	1 Pa = 1 N / m2 = 1 kg/(m·s2)	Named after Blaise Pascal.
...

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

External links

• www.example.com