EN ISO 80000-4:2019

Quantities and units - Part 4: Mechanics (ISO 80000-4:2019)

This document gives names, symbols, definitions and units for quantities of mechanics. Where appropriate, conversion factors are also given.

Größen und Einheiten - Teil 4: Mechanik (ISO 80000-4:2019)

Grandeurs et unités - Partie 4: Mécanique (ISO 80000-4:2019)

Le présent document donne les noms, les symboles, les définitions et les unités des grandeurs de la mécanique. Des facteurs de conversion sont également indiqués, s'il y a lieu.

Veličine in enote - 4. del: Mehanika (ISO 80000-4:2019)

Ta dokument podaja imena, simbole, definicije in enote za veličine s področja mehanike. Kadar je primerno, so navedeni tudi pretvorniki (pretvorni dejavniki).

General Information

• Status: Published
• Publication Date: 08-Oct-2019
• Withdrawal Date: 29-Apr-2020
• ICS: 01.060 - Quantities and units
• Technical Committee: CEN/SS F02 - Units and symbols
• Drafting Committee: CEN/SS F02 - Units and symbols
• Current Stage: 6060 - Definitive text made available (DAV) - Publishing
• Start Date: 09-Oct-2019
• Completion Date: 09-Oct-2019
• Ref Project: SIST EN ISO 80000-4:2019 - Quantities and units - Part 4: Mechanics (ISO 80000-4:2019)

Relations

• Replaces: EN ISO 80000-4:2013 - Quantities and units - Part 4: Mechanics (ISO 80000-4:2006)
• Effective Date: 16-Oct-2019

Standards Content (Sample)

SLOVENSKI STANDARD
SIST EN ISO 80000-4:2019
01-december-2019
Nadomešča:
SIST EN ISO 80000-4:2013
Veličine in enote - 4. del: Mehanika (ISO 80000-4:2019)
Quantities and units - Part 4: Mechanics (ISO 80000-4:2019)
Größen und Einheiten - Teil 4: Mechanik (ISO 80000-4:2019)
Grandeurs et unités - Partie 4: Mécanique (ISO 80000-4:2019)
Ta slovenski standard je istoveten z: EN ISO 80000-4:2019
ICS:
01.060 Veličine in enote Quantities and units
17.020 Meroslovje in merjenje na Metrology and measurement
splošno in general
SIST EN ISO 80000-4:2019 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 80000-4:2019

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SIST EN ISO 80000-4:2019


EN ISO 80000-4
EUROPEAN STANDARD

NORME EUROPÉENNE

October 2019
EUROPÄISCHE NORM
ICS 01.060 Supersedes EN ISO 80000-4:2013
English Version

Quantities and units - Part 4: Mechanics (ISO 80000-
4:2019)
Grandeurs et unités - Partie 4: Mécanique (ISO 80000- Größen und Einheiten - Teil 4: Mechanik (ISO 80000-
4:2019) 4:2019)
This European Standard was approved by CEN on 5 May 2019.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.





EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 80000-4:2019 E
worldwide for CEN national Members.

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SIST EN ISO 80000-4:2019
EN ISO 80000-4:2019 (E)
Contents Page
European foreword . 3

2

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SIST EN ISO 80000-4:2019
EN ISO 80000-4:2019 (E)
European foreword
This document (EN ISO 80000-4:2019) has been prepared by Technical Committee ISO/TC 12
"Quantities and units" in collaboration with Technical Committee CEN/SS F02 “Units and symbols” the
secretariat of which is held by CCMC.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by April 2020, and conflicting national standards shall be
withdrawn at the latest by April 2020.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 80000-4:2013.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 80000-4:2019 has been approved by CEN as EN ISO 80000-4:2019 without any
modification.

3

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SIST EN ISO 80000-4:2019

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SIST EN ISO 80000-4:2019
INTERNATIONAL ISO
STANDARD 80000-4
Second edition
2019-08
Quantities and units —
Part 4:
Mechanics
Grandeurs et unités —
Partie 4: Mécanique
Reference number
ISO 80000-4:2019(E)
©
ISO 2019

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SIST EN ISO 80000-4:2019
ISO 80000-4:2019(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2019
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Fax: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved

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SIST EN ISO 80000-4:2019
ISO 80000-4:2019(E)

Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
Bibliography .13
Alphabetical index .14
© ISO 2019 – All rights reserved iii

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SIST EN ISO 80000-4:2019
ISO 80000-4:2019(E)

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www. iso. org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www. iso.o rg/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www. iso
.org/iso/foreword. html.
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.
A list of all parts in the ISO 80000 and IEC 80000 series can be found on the ISO and IEC websites.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www. iso. org/members. html.
iv © ISO 2019 – All rights reserved

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SIST EN ISO 80000-4:2019
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/
© ISO 2019 – All rights reserved 1

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SIST EN ISO 80000-4:2019
ISO 80000-4:2019(E)

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):
1
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 :
0
ρ
d=
ρ
0
−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

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SIST EN ISO 80000-4:2019
ISO 80000-4:2019(E)

© ISO 2019 – All rights reserved 3
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
2
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

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SIST EN ISO 80000-4:2019
ISO 80000-4:2019(E)

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
2
where p is momentum (item 4-8).
IF= dt
∫
t
1
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

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SIST EN ISO 80000-4:2019
ISO 80000-4:2019(E)

© ISO 2019 – All rights reserved 5
Table 1 (continued)
Item No. Quantity Unit Remarks
N
...

SLOVENSKI STANDARD
oSIST prEN ISO 80000-4:2016
01-december-2016
9HOLþLQHLQHQRWHGHO0HKDQLND,62',6
Quantities and units - Part 4: Mechanics (ISO/DIS 80000-4:2016)
Größen und Einheiten - Teil 4: Mechanik (ISO/DIS 80000-4:2016)
Grandeurs et unités - Partie 4: Mécanique (ISO/DIS 80000-4:2016)
Ta slovenski standard je istoveten z: prEN ISO 80000-4
ICS:
01.060 9HOLþLQHLQHQRWH Quantities and units
17.020 Meroslovje in merjenje na Metrology and measurement
splošno in general
oSIST prEN ISO 80000-4:2016 en,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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oSIST prEN ISO 80000-4:2016

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oSIST prEN ISO 80000-4:2016
DRAFT INTERNATIONAL STANDARD
ISO/DIS 80000-4
ISO/TC 12 Secretariat: SIS
Voting begins on: Voting terminates on:
2016-10-21 2017-01-12
Quantities and units —
Part 4:
Mechanics
Grandeurs et unités —
Partie 4: Mécanique
ICS: 01.060
This document is circulated as received from the committee secretariat.
THIS DOCUMENT IS A DRAFT CIRCULATED
This draft is submitted to a parallel vote in ISO and in IEC.
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
IN ADDITION TO THEIR EVALUATION AS
ISO/CEN PARALLEL PROCESSING
BEING ACCEPTABLE FOR INDUSTRIAL,
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
STANDARDS MAY ON OCCASION HAVE TO
BE CONSIDERED IN THE LIGHT OF THEIR
POTENTIAL TO BECOME STANDARDS TO
WHICH REFERENCE MAY BE MADE IN
Reference number
NATIONAL REGULATIONS.
ISO/DIS 80000-4:2016(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
©
PROVIDE SUPPORTING DOCUMENTATION. ISO 2016

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oSIST prEN ISO 80000-4:2016
ISO/DIS 80000-4:2016(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2016, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. [phone]
Fax [phone]
[e-mail]
www.iso.org
ii © ISO 2016 – All rights reserved

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oSIST prEN ISO 80000-4:2016
ISO/DIS 80000-4:2016(E)
Contents Page
Foreword . iv
1 Scope. 1
2 Normative references . 1
3 Names, symbols, definitions and units of quantities . 1
Bibliography. 1


© ISO 2016 – All rights reserved iii

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oSIST prEN ISO 80000-4:2016
ISO/DIS 80000-4:2016(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national
standards bodies (ISO member bodies). The work of preparing International Standards is normally
carried out through ISO technical committees. Each member body interested in a subject for which a
technical committee has been established has the right to be represented on that committee.
International organizations, governmental and non-governmental, in liaison with ISO, also take part in
the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all
matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO's adherence to the WTO principles in the Technical
Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 12, Quantities and units.
This second edition cancels and replaces the first edition of ISO 80000-4:2006.
ISO 80000 consists of the following parts, under the general title Quantities and units:
 Part 1: General
 Part 2: Mathematics
 Part 3: Space and time
 Part 4: Mechanics
 Part 5: Thermodynamics
 Part 7: Light and Radiation
 Part 8: Acoustics
 Part 9: Physical chemistry and molecular physics
 Part 10: Atomic and nuclear physics
 Part 11: Characteristic numbers
 Part 12: Condensed matter physics
iv © ISO 2016 – All rights reserved

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oSIST prEN ISO 80000-4:2016
ISO/DIS 80000-4:2016(E)
IEC 80000 consists of the following parts (in collaboration with IEC/TC 25), under the general title
Quantities and units:
 Part 6: Electromagnetism
 Part 13: Information science and technology
 Part 14: Telebiometrics related to human physiology

© ISO 2016 – All rights reserved v

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oSIST prEN ISO 80000-4:2016

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oSIST prEN ISO 80000-4:2016
DRAFT INTERNATIONAL STANDARD ISO/DIS 80000-4 :2016(E)

Quantities and units — Part 4: Mechanics
1 Scope
ISO 80000-4 gives names, symbols and definitions for quantities and units of mechanics. Where
appropriate, conversion factors are also given.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest e dition of the referenced
document (including any amendments) applies.
ISO 80000-1:2009, Quantities and units — Part 1: General
ISO 80000-2:2009, Quantities and units — Part 2: Mathematics
ISO 80000-3:2006, Quantities and units — Part 3: Space and time

© ISO 2016 – All rights reserved
1

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oSIST prEN ISO 80000-4:2016
DRAFT INTERNATIONAL STANDARD ISO/DIS 80000-4 :2016(E)

3 Names, symbols, definitions and units of quantities
The names, symbols, definitions and units for quantities of mechanics are given on the following pages.
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
4-1 mass 𝑚 property of a body which expresses itself in terms of inertia kg
with regard to changes in its state of motion as well as its
attraction to other bodies
−3
m kg
4-2 mass density,  scalar quantity describing the distribution of mass with
respect to volume equal to the quotient of the mass dm (item
density
4-1) contained in an infinitesimal spherical 3D domain with
centre in point with position vector 𝒓 by the volume dV
(ISO 80000-3:2006, item 3-4) of this domain:
(𝒓) = d𝑚/d𝑉

3 −1
m kg
4-3 specific volume 𝑣 reciprocal of mass density
𝑣 = 1/𝜌
where 𝜌 is mass density (item 4-2)
4-4 relative mass density, 𝑑 quotient of mass density of a substance and mass density of a 1
reference substance under conditions that should be
relative density
specified for both substances
𝑑 = 𝜌/𝜌
0
where 𝜌 is the mass density (item 4-2) of a substance and 𝜌
0
is the mass density (item 4-2) of a reference substance
© ISO 2016 – All rights reserved
1

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oSIST prEN ISO 80000-4:2016
ISO/DIS 80000-4:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
−2
 m kg
4-5 surface mass density, scalar quantity describing the distribution of mass with The name “grammage” should not be
𝐴
respect to area equal to quotient of the mass d𝑚 (item 4-1) used for this quantity.
surface density
contained in an infinitesimal 2D domain dΓ round the end
point of the position vector 𝒓 with the area d𝐴 (ISO 80000-
3:2006, item 3-3):
 (𝒓) = d𝑚/d𝐴
𝐴
−1
 m kg
4-6 linear mass density, scalar quantity describing the distribution of mass with
𝑙
respect to length equal to quotient of the mass d𝑚 (item 4-1)
linear density
contained in an infinitesimal 1D domain dΓ round the end
point of the position vector 𝒓 with the length d𝑙 (ISO 80000-
3:2006, item 3-1.1):
d𝑚 = (𝒓) ⋅ d𝑙
𝑙
2
m kg
4-7.1 mass moment of 𝑰, 𝑱 scalar quantity describing the inertia of a rotating body This quantity should be distinguished
inertia,
from items 4-23, the second (axial or
2
∭ polar) moment of area. If there is a risk
 𝐽 = 𝑟 d𝑚
moment of inertia
Q
Q
𝑀
of confusion, the symbol 𝑱 should be
where 𝑀 is 3D domain containing considered body, 𝒓 is the used for item 4-7.1 and item 4-7.2 and 𝑰
𝑄
for items 4-21.
radial distance (ISO 80000-3:2006, item 3-1.6) from a Q-axis
from which the radial distance is determined and 𝑚 is mass
(item 4-1)
4-7.2 tensor of moment of 𝐽 tensor quantity describing the inertia of a rotating body
𝑖𝑘
inertia
2 2 2
𝐽 = ∭ (𝛿 (𝑥 + 𝑥 + 𝑥 ) − 𝑥 𝑥 )d𝑚
𝑖𝑗 𝑖𝑗 1 2 3 𝑖 𝑗
𝑀
where 𝑀 is 3D domain containing considered body, 𝑥 are
𝑖
cartesian coordinates (ISO 80000-3:2006, item 3-1.10), and
© ISO 2016 – All rights reserved
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oSIST prEN ISO 80000-4:2016
ISO/DIS 80000-4:2016(E)
Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
𝑚 is mass (item 4-1)
−1
m kg s
4-8 momentum
𝒑 product of mass 𝑚 (item 4-1) of a body and velocity 𝒗
(ISO 80000-3:2006, item 3-8.1) of its centre of mass
𝒑 = 𝑚𝒗
4-9.1 force 𝑭 additive vector quantity describing in classical mechanics N,
−2
interaction between two bodies or action of some fields to a
m kg s
body
4-9.2 weight 𝑭 product of mass 𝑚 (item 4-1) of a body and its local In colloquial language the name
g
acceleration 𝒈 of free fall (ISO 80000-3:2006, item 3-9.2)
“weight” continues to be used where
“mass” is meant. This practice should be
𝑭 = 𝑚 𝒈
g
avoided.
4-9.3 gravitational force 𝑭 force acting between two bodies caused by their masses  In classical physics, central attractive
force (item 4-9.1) between two point
masses (particles), of magnitude
𝐺𝑚 𝑚
1 2
𝐹 =
2
𝑟
where 𝐺 is the gravitational constant
(ISO 80000-1, item ??), 𝑚 and 𝑚 are
1 2
the masses (item 4-1) of those particles
and 𝑟 is the distance (ISO 80000-
3:2006, item 3-1.9) between them.
4-9.4 static friction force, 𝑭 force resisting the motion before a body starts to slide on a The relative speed of body to surface in
surface the contact point is in this case equal to
static friction
zero. The actual values of magnitude
and direction static friction force is so
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that the sum of all acting forces is equal
to zero.
4-9.5 kinetic friction force, 𝑭 force resisting the motion when a body slides on a surface While sliding, the relative speed of body
to surface in the contact point is greater
dynamic friction force
than zero.
4-9.6 rolling friction force, 𝑭 force resisting the motion when a body rolls on a surface While rolling, the relative speed of body
to surface in the contact point is equal
rolling resistance,
to zero.
rolling drag
4-9.7 drag force 𝑭 force resisting the motion when a body moves in a fluid See item 4-10.
D
4-9.8 spring force 𝑭 force caused by a spring  Spring force is often taken as linear:
𝑭 = −𝑘𝒓
where 𝑘 is rigidity (item 4-11).
4-10 drag factor, factor proportional to magnitude 𝐹 of the drag force (item 1 The name “coefficient” is widely used,
𝐶
D
D
4-9.7) of a body moving in a fluid, dependent on the shape but incorrect because it should not be
drag coefficient
and speed 𝑣 (ISO 80000-3:2006, item 3-8.1) of a body, by used for quantities with dimension 1.
1
2
𝐹 = 𝐶 𝜌𝑣 𝐴
𝐷 D
2
where 𝜌 is mass density (item 4-2) of fluid and 𝐴 is cross-
section area of body
−2
kg s
4-11 rigidity for linear spring force, negative coefficient of proportionality If vectors of spring force 𝑭 and
𝑘
between spring force 𝑭 (item 4-9.8) and displacement 𝒅 displacement 𝒅 of the free end of linear
(ISO 80000-3:2006, item 3-1.12) of its free end, thus
spring have different directions, rigidity
can be expressed by tensor 𝑘 , where
𝑖𝑗
𝑭 = −𝑘𝒅
∑
𝐹 = − 𝑘 𝑑
𝑖 𝑖𝑗 𝑗
𝑗
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Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
For a time interval [𝑡 ,𝑡 ],
4-12 impulse 𝑰 quantity describing the effect of force acting during a time
Ns, 1 2
interval: −1
( ) ( ) ( )
𝑰 𝑡 ,𝑡 = 𝒑 𝑡 − 𝒑 𝑡 = Δ𝒑
m kg s
1 2 1 2
𝑡
2
where p is momentum (item 4-8).
∫
𝑰 = 𝑭 d𝑡
𝑡
1
where F is force (item 4-9.1), t is time (ISO 80000-3:2006,
item 3-7) and [𝑡 ,𝑡 ] is considered time interval
1 2
2 −1
m kg s
4-13 angular momentum 𝑳 vector product: The angular momentum depends on the
origin of the coordinate system.
𝑳 = 𝒓 × 𝒑
This definition also applies to the term
where r is position vector (ISO 80000-3:2006, item 3-1.11)
"moment of momentum".
and p is momentum (item 4-8)
4-14.1 moment of force 𝑴 vector product: The moment of force depends on the
Nm,
2 −2 origin of the coordinate system.
𝑴 = 𝒓 × 𝑭
m kg s
The bending moment of force is
where r is position vector (ISO 80000-3:2006, item 3-1.11)
denoted by 𝑴
b
and F is force (item 4-9.1)
4-14.2 torque 𝑇, 𝑀 scalar product: For example torque is the twisting
𝑄
moment of force with respect to the
𝑇 = 𝑴 ⋅ 𝒆
Q
longitudinal axis of a beam or shaft.
where 𝑴 is moment of force (item 4-14.1) and 𝒆 is unit
Q
vector of direction with respect to which the torque is
considered
For a time interval [𝑡 ,𝑡 ],
1 2
4-15 angular impulse 𝑯 vector quantity describing the effect of moment of force Nms,
during a time interval: 2 −1
m kg s
( ) ( ) ( )
𝑯 𝑡 , 𝑡 = 𝑳 𝑡 − 𝑳 𝑡 = ∆𝑳
𝑡
2 1 2 2 1
𝑯(𝑡 ; 𝑡 ) = ∫ 𝑴(𝑡) d𝑡
1 2
𝑡
1
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Quantity Unit
Item
Remarks
No.
Name Symbol Definition Symbol
where M is moment of force (item 4-14.1), t is time where 𝑳 is angular momentum.
(ISO 80000-3:2006, item 3-7) and [𝑡 ,𝑡 ] is considered time
1 2
interval

4-16.1 pressure 𝑝 quotient of the component of a force normal to an area and Pa,

that area −2
N m ,
( )⁄ −1 −2
𝑝 = 𝒆 𝑭 𝐴
𝑛
m kg s
where 𝒆 is unit vector of the surface normal and F is a force
𝑛
(item 4-9.1) and A is an area (ISO 80000-3:2006, item 3-3)

⊝
4-16.2 standard pressure conventionally chosen value of pressure This value corresponds to the 760 mm
𝑝 , 𝑝 , 𝑝°
0
of mercury column in a Torricelli
𝑝 = 101 325 Pa
0
manometer under temperature 𝑇 =
0
0 °C and acceleration 𝒈 of free fall
(ISO 80000-3:2006, item 3-9.2).
 𝑝 conventionally chosen value of pressure In particular cases, when this value is
0
taken; it should be stressed separately
𝑝 = 100 000 Pa
0
4-16.3 gauge pressure 𝑝 pressure 𝑝 (item 4-16.1) decremented by ambient pressure Often, 𝑝 is chosen either as a
e amb
𝑝 (item 4-16.1) standard pressure (item 4-16.2)
amb
𝑝 = 𝑝 − 𝑝 Gauge pressure is positive or negative.
e amb
4-16.4 normal stress 𝜎 scalar quantity describing surface action of a force into a The surface element is generally a
body equal to virtual surface.
𝜎 = d𝐹 /d𝐴
n
where d𝐹 is the normal component of force (item 4-9.1) and
n
d𝐴 is the area(ISO 80000-3:2006, item 3-3) of the surface
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