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Applied Mathematics B154 - Full A2 & A3 Summary

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Course
Applied Mathematics B154 (20753154)

Institution
Stellenbosch University (SUN)

This is a full summary of Applied Mathematics B154 from the textbook and Lecture slides. This summary has all the formulas as well as hints on what formulas to use for specific types of questions.

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Uploaded on October 26, 2024
Number of pages 7
Written in 2024/2025
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APPLIED MATHS 154
Newton's 2nd law
Equation of motion
Equationsystemofparticles
A 2 S UMM A R Y Equationsrectangularcoordina
NormalbTangential componen
Polarcoordinates cylindrical
Lf
ffILE.FI OF A PARTICLE FORCE
AND ACCELERATION
relationbetweenthe change in motion andthe forces causing this change

VENTON'SFIRSTLAW everybody perseveres in its state of rest oruniformmotion in aright line
change its state of rest
NEWTON'S SECOND Law s YEP p
when an unbalancedforceacts on a particle the particle will accelerate in the
direction of the force with a magnitude that is proportional to the force

EE ma
mass is the inertia of the particle
N kg m 52 to accelerate inertiaagainst acceleration
VENTON'S THIRDLAW

2
t.cm aYsi s nYn rsof particles

W mg N g 9.81m52 ONLY GRAVITATIONALFORCECONSIDERED

33.22 EQUATIONS OF MOTION
if FR EF 0 acceleration zero
F ma it forces acting on a particle particle remains at rest or move
along a straight line at a constant
INERTIALREFERENCE FRAME velocity
Frameeitherfixed or translates with a
constantvelocity
observer accelerate measurements of
particleacceleration willbethe samefrom any reference of this type
3333EQUATIONS OFMOTIONFORASYSTEMOF PARTICLES
no restriction in way particles are connected
qq.mg fit.fi migi
instant considered arbituary i th particle
mass mi EF.itE.fi migi
internal force fi Fr
resultant external force Fi gravitational electric magnetic
unbalanced force on a particle causes it to accelerate
sum externalforces acting on the system of particles is to total mass
of the particle acceleration equation of motion to a body that is represented as a
single particle
EE MAG

,133.4 EQUATIONS OFMOTIONRECTANGULARCOORDINATES 4.2 Mmm

movesrelative to a y z inertialframe
forces actingon particle as well as its acceleration can be expressedas i.j.is components

EFai EFyj Fzk m and ayj.t.az left side rightside

1133
55 EQUATIONSOFMOTIONNORMALANDTANGENTIAL COMPONENTS notmftibon.in
binormaldirection
articlemovesalong a curvedpathknown Normal tangential binomialdirections
Fn centripetalforce ban Ft 0 speedincreases
Eft co speeddecreases
ftp.imminimmpi rati

EQQUATTIIOONVSSOOFFMOOTTI.COM CCYYUIINVDDRRIICCAALLCCOOOORRDDIINVAATTE.ES

All Forcesacting on aparticle resolvedintocylindricalcoordinates components

Esoyo Faye maryrtmaoyotmazt.bz

imma
Fz maz mi
If particleconstrained to r o plane Eq 132apply
Normalforce 1 to thetangent of the path
FrictionalForceactsalongtangent in OPPOSITE directionofmotion

an 4 I do EXTENDED RADIALLINETOTANGENTOFCURVE

, SUMMARY CHAPTER 1133

NEWTON'S2ND LAW
when an unbalanced force acts on a particle the particle will accelerate in the direction
of the force with a magnitude that is proportional to the force

E ma W mgin g 9.81 m s
EQUATION OF MOTION
SYSTEM OF PARTICLEESS

EE M.GG

EQUATION OF MOTIONRREECCTTAANGULLAARRCCOORRDDIINNAATTEEN.ly 2
EQUATIONSOF MOTION KINEMATICS useonce a foundfrom EE ma
acceleration function oftime
FRICTION Ff UKN
opposesmotion relativeto surface as It v velocity position

SPRING acceleration functionof displacement

1 deformed length ads vav velocity as function of position
to undeformed length
acceleration is constant

EQUATIONSOFMOTION E n b ᵗ positionof
up'ggi
NORMAL
BTTAANGEENNTTIAAL ae.fi
time rateofchange ofmagnitude an
I.miltsas'h 9a dfiintYpafin'stiffer of curvature
shop hire speed
h mpi

QQUATTIIONNSSOOFFMOOTTI.NU CCYYLIINVDDRRIICCAALLCCOOOORRDDIINAATTE.ES
r 0,2

Fr mar m i ro
Fo mao m rotaro
T2 maz mi

line
anU.at do99hgb 19nergdial

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Applied Mathematics B154 - Full A2 & A3 Summary

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