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These equations express mathematically that, in the case of an object that moves along a circular path with a changing speed, the acceleration of the body may be decomposed into a perpendicular component that changes the direction of motion ( the centripetal acceleration ), and a parallel, or tangential component, that changes the speed.

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## Some Related Sentences

These and equations

__These__range from simplified forms

**of**

**the**first-principles

__equations__

**that**are easier

**or**faster to solve

**,**to approximations limiting

**the**size

**of**

**the**system

**(**for example

**,**periodic boundary conditions

**),**to fundamental approximations to

**the**underlying

__equations__

**that**are required to achieve any solution to them at all

**.**

__These__two

__equations__can

**be**differentiated

**and**combined

**in**various ways to produce

**the**following data:

__These__

__equations__

**of**state were also previously published by

**the**Soviet physicist Yakov Frenkel

**in**1928

**,**together

**with**some other remarks on

**the**physics

**of**degenerate matter

**.**

__These__

__equations__can

**be**used as

**the**starting point

**in**

**the**analysis

**of**

**a**flexible chain acting under any external force

**.**

__These__

__equations__specify how

**the**geometry

**of**space

**and**time is influenced by whatever matter is present

**,**

**and**form

**the**core

**of**Einstein's general theory

**of**relativity

**.**

__These__

__equations__are notoriously difficult to solve

**,**but

**in**many instances approximations suffice for

**a**good description

**of**lifting airfoils

**.**

__These__types

**of**integrals seem first to have attracted Laplace's attention

**in**1782 where he was following

**in**

**the**spirit

**of**Euler

**in**using

**the**integrals themselves as solutions

**of**

__equations__

**.**

__These__same interpolation formulas nevertheless continue to

**be**used as part

**of**

**the**software algorithms for solving differential

__equations__

**.**

__These__

__equations__explain quantitatively how quarks can bind together

**into**protons

**and**neutrons

**(**

**and**all

**the**other hadrons ).

__These__

__equations__

**of**

**motion**are then supplemented by commutation relations derived from

**the**canonical quantization procedure described below

**,**thereby incorporating quantum mechanical effects

**into**

**the**behavior

**of**

**the**field

**.**

__These__observations corroborated Alexander Friedman's 1922 work

**,**

**in**which he derived

**the**famous Friedmann

__equations__

**.**

__These__

__equations__demonstrate

**that**

**the**simple harmonic

**motion**is isochronous

**(**

**the**period

**and**frequency are independent

**of**

**the**amplitude

**and**

**the**initial phase

**of**

**the**

**motion**).

__These__

__equations__were verified by experiment by Heinrich Hertz

**in**1887

**,**

**and**

**the**wave theory became widely accepted

**.**

These and express

__These__things both

__express__

**and**

**,**at

**the**same time

**,**continue contributing to

**,**their identity diffusion

**in**

**an**area

**that**could have become

**a**source

**of**developing dignity

**and**self-certainty

**.**

__These__nonce orders all

__express__

**the**" speaking architecture "

**(**architecture parlante )

**that**was taught

**in**

**the**Paris courses

**,**most explicitly by Étienne-Louis Boullée

**,**

**in**which sculptural details

**of**classical architecture could

**be**enlisted to speak symbolically

**,**

**the**better to

__express__

**the**purpose

**of**

**the**structure

**and**enrich its visual meaning

**with**specific appropriateness

**.**

__These__minutes correspond to

**the**Latin diei scrupulis

**,**

**and**used to

__express__periods

**of**planetary motions

**.**

__These__outcomes occur because giving some passengers full

__express__services means bypassing often large numbers

**of**passengers at intermediate stations

**along**

**the**corridors

**.**

__These__are quantities

**that**

__express__

**the**local state

**of**

**the**system

**,**besides

**the**usual local thermodynamic variables ;

**in**

**a**sense such variables might

**be**seen as expressing

**the**' memory '

**of**

**the**materials

**.**

__These__words must

**be**factual yet entertaining as

**the**Count states

**,**“ then

**,**it is necessary to arrange what is to

**be**said

**or**written

**in**its logical order

**,**

**and**after

**that**to

__express__it well

**in**words

**that**

**,**if I am not mistaken

**,**should

**be**appropriate

**,**carefully chosen

**,**clear

**and**well formed

**,**but above all

**that**are still

**in**popular use "

**(**Courtier 77 ).

__These__myths also

__express__some hope

**that**

**the**idyllic state

**of**affairs they describe is not irretrievably

**and**irrevocably lost to mankind

**,**

**that**it can

**be**regained

**in**some way

**or**other

**.**

__These__words

**and**terms were used because

**of**their familiarity

**,**but more so because

**in**most cases there were no equivalent terms

**in**

**the**vernacular which could

__express__

**the**Jewish concepts

**or**describe

**the**objects

**of**cultural significance

**.**

__These__complications mean

**that**there are three common ways to

__express__

**a**polynomial as

**an**integer:

**the**first two

**,**which are mirror images

**in**binary

**,**are

**the**constants found

**in**code ;

**the**third is

**the**number found

**in**Koopman's papers

**.**

The

**path**loss for**the**first ten kilometers**may****be**150 -- 190 dB**(**Note:__These__values are very approximate**and**are given here only as**an**illustration**of****the**range**in**which**the**numbers used to__express__**the****path**loss values can eventually**be****,**these are not definitive**or**binding figures --**the****path**loss**may****be**very different for**the**same distance**along**two different paths**and**it can**be**different even**along****the**same**path**if measured at different times**.**
"

__These__symbols__express__**a**self-view**of****the**Prieneians as**a**maritime democracy aligned**with**Athens but located**in**Asia**.**__These__demonstrate his attempt to

__express__

**the**tension between

**the**static stone

**and**

**the**dynamic desires

**of**

**the**figures represented emerging

**into**solidity from it

**.**

__These__included

__express__coach

**(**Transport Act 1980

**),**British Telecom

**(**completed

**in**1984

**),**privatisation

**of**London bus services

**(**1984

**),**local bus services

**(**Transport Act 1985 )

**and**

**the**railways

**(**1993 ).

__These__cells are also known as CD4 < sup >+</ sup > T cells because they

__express__

**the**CD4 protein on their surface

**.**

__These__cells are also known as CD8 < sup >+</ sup > T cells since they

__express__

**the**CD8 glycoprotein at their surface

**.**

__These__self-antigens are expressed by thymic cortical epithelial cells

**that**

__express__Activation-Induced

**(**Cytidine ) Deaminase on both MHC molecules on

**the**surface

**of**cortical cells

**.**

__These__

**,**

**along**

**with**

**the**similar British Rail Class 86 | Class 86 formed

**the**backbone

**of**

__express__passenger services on

**the**WCML from

**the**1970s until

**the**2000s

**.**

"

__These__phrases__express__**the**idea**that****the**totem always accompanies**,**belongs to**,****and**stands behind one as**a**guide**and**warner**of**dangers**.**0.151 seconds.