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INTERNATIONAL ISO
STANDARD 80000-4
Second edition
2019-08
Quantities and units —
Part 4:
Mechanics
Grandeurs et unités —
Partie 4: Mécanique
Reference number
©
ISO 2019
© ISO 2019
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ii © ISO 2019 – All rights reserved
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
Bibliography .13
Alphabetical index .14
Foreword
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This document was prepared by Technical Committee ISO/TC 12, Quantities and units, in collaboration
with Technical Committee IEC/TC 25, Quantities and units.
This second edition cancels and replaces the first edition (ISO 80000-4:2006), which has been
technically revised.
The main changes compared to the previous edition are as follows:
— the table giving the quantities and units has been simplified;
— some definitions and the remarks have been stated physically more precisely.
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Any feedback or questions on this document should be directed to the user’s national standards body. A
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iv © ISO 2019 – All rights reserved
INTERNATIONAL STANDARD ISO 80000-4:2019(E)
Quantities and units —
Part 4:
Mechanics
1 Scope
This document gives names, symbols, definitions and units for quantities of mechanics. Where
appropriate, conversion factors are also given.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
Names, symbols, definitions and units for quantities used in mechanics are given in Table 1.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https: //www .iso .org/obp
— IEC Electropedia: available at http: //www .electropedia .org/
2 © ISO 2019 – All rights reserved
Table 1 — Quantities and units used in mechanics
Item No. Quantity Unit Remarks
Name Symbol Definition
4-1 mass m property of a body which expresses itself in terms of iner- kg The kilogram (kg) is one of the seven
tia with regard to changes in its state of motion as well as base units (see ISO 80000-1) of the
its gravitational attraction to other bodies International System of Units, the SI.
See also IEC 60050-113.
−3
4-2 mass density, quantity representing the spatial distribution of mass of a kg m
ρ , ρ
m
continuous material:
density
dm
ρ()r =
dV
where m is mass of the material contained in an infinitesi-
mal domain at point r and V is volume of this domain
−1 3
4-3 specific volume v kg m
reciprocal of mass density ρ (item 4-2):
v=
ρ
4-4 relative mass density, d 1 Conditions and material should be
quotient of mass density of a substance ρ and mass
specified for the reference substance.
relative density
density of a reference substance ρ :
ρ
d=
ρ
−2
4-5 surface mass density, quantity representing the areal distribution of mass of a kg m The name “grammage” should not be
ρ
A
continuous material: used for this quantity.
surface density
dm
ρ ()r =
A
dA
where m is the mass of the material at position r and A is
area
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
−1
4-6 linear mass density, quantity representing the linear distribution of mass of a kg m
ρ
l
continuous material:
linear density
dm
ρ ()r =
l
dl
where m is the mass of the material at position r and l is
length
4-7 moment of inertia tensor (ISO 80000-2) quantity representing rotational kg m The calculation of the value requires
J
inertia of a rigid body relative to a fixed centre of rotation an integration.
expressed by the tensor product:
LJ= ωω
where L is angular momentum (ISO 80000-3) of the body
relative to the reference point and ωω is its angular velocity
(ISO 80000-3)
−1
4-8 momentum kg m s
p product of mass m (item 4-1) of a body and velocity v
(ISO 80000-3) of its centre of mass:
p=mv
4-9.1 force vector (ISO 80000-2) quantity describing interaction be- N
F
tween bodies or particles
−2
kg m s
4-9.2 weight force (item 4-9.1) acting on a body in the gravitational field N In colloquial language, the name
F
g
of Earth: “weight” continues to be used where
−2
kg m s
“mass” is meant. This practice should
Fg=m
be avoided.
g
where m (item 4-1) is the mass of the body and g is the Weight is an example of a gravitational
force. Weight comprises not only the
local acceleration of free fall (ISO 80000-3)
local gravitational force but also the
local centrifugal force due to the rota-
tion of the Earth.
4-9.3 static friction force, force (item 4-9.1) resisting the motion before a body starts N For the static friction coefficient, see
F
s
to slide on a surface item 4-23.1.
−2
static friction kg m s
4-9.4 kinetic friction force, force (item 4-9.1) resisting the motion when a body slides N For the kinetic friction factor, see
F
μ
on a surface item 4-23.2.
−2
dynamic friction force kg m s
4 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
4-9.5 rolling resistance, force (item 4-9.1) resisting the motion when a body rolls on N For the rolling resistance factor, see
F
rr
a surface item 4-23.3.
−2
rolling drag, kg m s
rolling friction force
4-9.6 drag force force (item 4-9.1) resisting the motion of a body in a fluid N For the drag coefficient, see item 4-23.4.
F
D
−2
kg m s
4-10 impulse vector (ISO 80000-2) quantity describing the effect of force N s For a time interval [t , t ],
1 2
I
acting during a time interval:
−1
kg m s
Iptt, = tt−pp=D
() () ()
12 12
t
where p is momentum (item 4-8).
IF= dt
∫
t
where F is force (item 4-9.1), t is time (ISO 80000-3) and
[t , t ] is considered time interval
1 2
2 −1
4-11 angular momentum vector (ISO 80000-2) quantity described by the vector kg m s
L
product:
Lr=×p
where r is position vector (ISO 80000-3) with respect to
the axis of rotation and p is momentum (item 4-8)
4-12.1 moment of force vector (ISO 80000-2) quantity described by the vector N m The bending moment of force is
M
product:
2 −2 denoted by M .
kg m s
b
Mr=×F
where r is position vector (ISO 80000-3) with respect to
the axis of rotation and F is force (item 4-9.1)
4-12.2 torque T, M quantity described by the scalar product: N m For example, torque is the twisting
Q
moment of force with respect to the
2 −2
kg m s
T=⋅Me
longitudinal axis of a beam or shaft.
Q
where M is moment of force (item 4-12.1) and e is unit
Q
vector of direction with respect to which the torque is
considered
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
4-13 angular impulse vector (ISO 80000-2) quantity describing the effect of mo- N m s For a time interval [t , t ],
1 2
H
ment of force during a time interval:
2 −1
kg m s
HLtt, = tt−LL=D
() () ()
12 21
t
where L is angular momentum.
HMtt; = dt
()
12 ∫
t
where M is moment of force (item 4-12.1), t is time
(ISO 80000-3) and [t , t ] is considered time interval
1 2
4-14.1 pressure p quotient of the component of a force normal to a surface Pa
and its area:
−2
N m
eF −1 −2
kg m s
n
p=
A
where e is unit vector of the surface normal, F is force
n
(item 4-9.1) and A is area (ISO 80000-3)
4-14.2 gauge pressure pressure p (item 4-14.1) decremented by ambient Pa
p Often, p is chosen as a standard
e amb
pressure p : −2
N m
amb
pressure.
−1 −2
kg m s
pp=−p
eamb
Gauge pressure is positive or negative.
4-15 stress tensor (ISO 80000-2) quantity representing state of ten- Pa Stress tensor is symmetric and has
σ
sion of matter three normal-stress and three shear-
−2
N m
stress (Cartesian) components.
−1 −2
kg m s
4-16.1 normal stress scalar (ISO 80000-2) quantity describing surface action of Pa A couple of mutually opposite forces of
σ , σ
n
a force into a body equal to: magnitude F acting on the opposite
−2
N m
surfaces of a slice (layer) of homoge-
−1 −2
dF
kg m s nous solid matter normal to it, and
n
σ =
n
evenly distributed, cause a constant
dA
normal stress σ =FA in the slice
where F is the normal component of force (item 4-9.1) and
n
n
A is the area (ISO 80000-3) of the surface element
(layer).
6 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
4-16.2 shear stress scalar (ISO 80000-2) quantity describing surface action of Pa A couple of mutually opposite forces of
τ , τ
s
a force into a body equal to: magnitude F acting on the opposite
−2
N m
surfaces of a slice (layer) of homoge-
dF −1 −2
nous solid matter parallel to it, and
kg m s
t
τ =
s
evenly distributed, cause a constant
dA
shear stress τ=FA/ in the slice (layer).
where F is the tangential component of force (item 4-9.1)
t
and A is the area (ISO 80000-3) of the surface element
4-17.1 strain εε tensor (ISO 80000-2) quantity representing the deforma- 1 Strain tensor is symmetric and has
tion of matter caused by stress three linear-strain and three shear
strain (Cartesian) components.
4-17.2 relative linear strain 1
ε , (e)
quotient of change in length Dl (ISO 80000-3) of an object
and its length l (ISO 80000-3):
Dl
ε=
l
4-17.3 shear strain 1
γ
quotient of parallel displacement Dx (ISO 80000-3) of
two surfaces of a layer and the thickness d (ISO 80000-3)
of the layer:
Dx
γ =
d
4-17.4 relative volume strain 1
ϑ
quotient of change in volume DV (ISO 80000-3) of an
object and its volume V (ISO 80000-3):
DV
ϑ=
V
4-18 Poisson number 1
μ , (v)
quotient of change in width Db (width is defined in
ISO 80000-3) and change in length Dl (length is defined in
ISO 80000-3) of an object:
Db
μ=
Dl
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
4-19.1 modulus of elasticity, E, E , Y Pa Conditions should be specified (e.g.
m
quotient of normal stress σ (item 4-16.1) and relative
adiabatic or isothermal process).
−2
Young modulus N m
linear strain ε (item 4-17.2):
−1 −2
kg m s
σ
E=
ε
4-19.2 modulus of rigidity, G Pa Conditions should be specified (e.g.
quotient of shear stress τ (item 4-16.2) and shear strain γ
isentropic or isothermal process).
−2
shear modulus N m
(item 4-17.3):
−1 −2
kg m s
τ
G=
γ
4-19.3 modulus of K, K , B negative of the quotient of pressure p (item 4-14.1) and Pa Conditions should be specified (e.g.
m
compression, isentropic
...