This was the overview of information given in the first half of 1/2013 semester in the physics class on September 18, 2013.

1. P!h!!!"! c!î!
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Worawarong Rakreungdet, Physics Dept., KMUTT
Vectors
Weekly Goal: Vectors.Adding and multiplying vectors.
Resource: HyperPhysics:
Physics concept maps.
http://hyperphysics.phy-
astr.gsu.edu/hbase/hframe.html
Class Textbook:
D. Halliday, R. Resnick and J.
Walker, Fundamental of Physics,
John Wiley & Son Inc., New
York, USA.
(based on graphics) (based on vector components) (based on polar forms)
Vector Calculus
• The “del,” the
collection of
partial derivatives
• Gradient:
• Divergence:
• Curl:
• LaPlacian:
Vector Product
Vector Addition
Scalar Product
B will be placed on the x-axis
and both A and B in the xy plane
ˆi ˆe1
ˆj ˆe2
ˆk ˆe3
1, if i = j
0, if i = j
ij =
Extra:
ˆei · ˆej = ij
ijk =
+1##if##(i,j,k)#is#(1,2,3),#(3,1,2)#or#(2,3,1)##
.1##if##(i,j,k)#is#(3,2,1),#(1,3,2)#or#(2,1,3)##
0##otherwise:##i = j##or##j = k or k = i#
⇥a ⇥b = ⇥c; ci =
3
j,k=1
ijkajbk
GEN 103 General Physics for (Mechanical) Engineering Students
https://www.facebook.com/groups/kmutt.phy103.ME.56/

2. P!h!!!"! c!î!
Ph!" îc #
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Ph!" îc #
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Worawarong Rakreungdet, Physics Dept., KMUTT
Newton’s Laws and the Causes of motion
Important Websites:
Class URL: all information about PHY 103 (2/2011)
http://webstaff.kmutt.ac.th/~worawarong.rak/classes/
2554-2/PHY103/home.html
HyperPhysics: Physics concept maps, nice illustration.
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
Standard Newton’s Laws Problems
nX
i=1
Fi = ma
Free-Body Diagram
A free-body diagram is a sketch of an
object of interest with all the
surrounding objects stripped away
and all of the forces acting on the
body shown.The drawing of a free-
body diagram is an important step in
the solving of mechanics problems
since it helps to visualize all the
forces acting on a single object.The
net external force acting on the
object must be obtained in order to
apply Newton's Second Law to the
motion of the object.
Newton’s Law
1st Law:
nX
i=1
Fi = 0; ! v = constant
Faction = Freaction
nX
i=1
Fi = 0; ! v = constant
Newton’s Law
2nd Law:
Newton’s Law
3rd Law:
GEN 103 General Physics for (Mechanical) Engineering Students
https://www.facebook.com/groups/kmutt.phy103.ME.56/

3. Collision'and'Impulse'
• From''''''''''''''''''''''','the'net'change'of'the'system'due'
to'collision'is''
'the'le8'side'of'the'equa:on'
'is'a'measure'of'both'the'magnitude'and'dura:on'of'
the'collisional'force,'defined'as'the'impulse(of'the'
collision.'
dp = F(t)dt
tf
ti
dp(t) =
tf
ti
F(t)dt
tf
ti
dp(t) = pf pi = p
Impulse = p =
tf
ti
F(t)dt
P!h!!!"! c!î!
Ph!" îc #
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Ph!" îc #
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Worawarong Rakreungdet, Physics Dept., KMUTT
System of Particles / Center of mass concept
Center of Mass (COM):The point that moves as though:
1. all of the system’s mass were concentrated there
2. all external forces that create translation were applied there
Two-point system
Point&source&
F
Finite&source&
H&
L&
F
rcom =
n
i=1 miri
n
i=1 mi
rcom =
rdm
dm
=
1
M
⇥
rdm
General definition
Note: For simplicity, we will always assume that an object is uniform in this course
The$mo'on$of$the$c.o.m.$of$any$system$of$par'cles$is$governed$by$
$$
Fnet = Macom
All$external$force.$Forces$
on$one$part$of$the$system$
from$another$part$of$the$
systems$(internal$forces)$
are$not$included$here.$
Total$mass.$No$mass$
enters$or$leaves$the$
system$as$it$moves.$
(M$=$constant).$This$
is$referred$to$as$a$
closed$system$$
Accelera'on$of$the$c.o.m.$
of$the$system.$There$is$no$
informa'on$regarding$
any$other$point$of$the$
system$$
Newton'2nd'Law'of'mo.on'
Linear'momentum' p = mv
For a particle P = Mvcom
Fnet =
dP
dt
For a system of particles
same area under
the curve
pfx pix =
tf
ti
Fx(t)dt
e.g. along the x-direction
p = Favg tWe can simplify the impulse using
Conserva)on*of*linear*momentum*
Fnet =
dP
dt
= 0 P = constant Pi = Pf (closed,)isolated)system))
Momentum(and(Kine-c(Energy(in(Collisions(
• Conserva-on(of(linear(momentum(
• Conserva-on(of(total(energy(
• Considering(the(kine-c(energy(of(the(system,(
– If(the(kine-c(energy(is(conserved,(then(the(collision(is(elas%c.(
– If(the(kine-c(energy(is(not(conserved,(then(the(collision(is(inelas%c.(
Pf = Pi
Ef = Ei
(for(a(closed,(isolated(system)(
(always(true!)(
Conserved/=/Has/the/same/value/both/before/and/a7er/
m1v1i = m1v1f + m2v2f
1
2
m1v2
1i =
1
2
m1v2
1f +
1
2
m2v2
2f
Example: Elastic Collision in 1 dimension
v2f =
2m1
m1 + m2
v1i
v1f =
m1 m2
m1 + m2
v1i
Extra: completely
inelastic = largest
energy lost in the
system.This will
result in two
bodies stick
together
GEN 103 General Physics for (Mechanical) Engineering Students
https://www.facebook.com/groups/kmutt.phy103.ME.56/

4. The$Kine(c$Energy$of$Rolling$
must$take$into$account$both$rota(on$and$transla(on$
1
2
Icom
2 1
2
Mv2
com+ = (K.E.)rolling
rota%onal(kine(c$energy$
due$to$rota(ons$about$
its$center$of$mass$
transla%onal(kine(c$energy$
due$to$transla(on$of$its$
center$of$mass$
Kine(c$Energy$(K.E.)$
of$a$rolling$object$
P!h!!!"! c!î!
Ph!" îc #
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Ph!" îc #
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Worawarong Rakreungdet, Physics Dept., KMUTT
Rotation + Rolling
I = mir2
i I = r2
dm
P =
dW
dt
= ⇥ (Power, rotation about a fixed axis)
K =
1
2
I 2
f
1
2
I 2
i = W. (Work-Kinetic Theory for Rotation)
⇥ = ⇥r ⇥F
⇤⇥net = I⇤
l = r p
L = I
⇥net =
d⇥L
dt
= 0
L = constant
TORQUE
ANGULAR MOMENTUM
If
(conserv. of ang. momentum)
GEN 103 General Physics for (Mechanical) Engineering Students
https://www.facebook.com/groups/kmutt.phy103.ME.56/

5. p =
F
A
Pascal’s'Principle'and'the'Hydraulic'Lever'
Considering'the'work'done'by'the'output'piston,'
W = Fodo = Fi
Ao
Ai
⇥
di
Ai
Ao
⇥
= Fidi
Work'done'by'the'output'piston'
in'li=ing'the'load'placed'on'it'
Work'done'on'the'input'
piston'by'the'applied'force'
Hydraulic*Lever*
Pascal’s*Principle:'A'change'in'the'pressure'applied'to'an'enclosed'incompressible'fluid'is'
transmiCed'undiminished'to'every'porDon'of'the'fluid'and'to'the'walls'of'its'container.”'
P!h!!!"! c!î!
Ph!" îc #
$!!"#$$%
Ph!" îc #
$!!"#$$%
Worawarong Rakreungdet, Physics Dept., KMUTT
Fluid Dynamics
Av1 = Av2
This%rela*onship%also%apply%to%any%so0called%tube%of%flow.%%
Any%imaginary%
flow%whose%
boundary%consists%
of%streamlines.%
Volume%flow%rate% Mass%flow%rate%
RV = Av = const. Rm = RV = const.
Equa*on%of%
Con*nuity%
Bernoulli’s+Equa/on+A+principle+of+fluid+flow+based+on+
conserva/on+of+energy+
p +
1
2
v2
+ gy = constant
Streamline*represents*
the*fluid*path*
Flow*of*Ideal*Fluids*
“Real*Fluids”*
Turbulence)flow)of)a)fluid)around)an)
obstacle)
h9p://www.jet.efda.org/pages/focus/
modelling/images/turbulence.jpg*
Real*fluids*****!*very*complicated**
* ***********!*not*well*understood*
Thus*we’ll*only*focus*on*“ideal*fluids”*
Ideal*fluids****!**
1. steady*flow*(***************)*
2. Incompressible*flow*(******************)*
3. Nonviscous*flow*(no*drag*force)*
4. IrrotaLonal*flow*(no*rotaLon)*
dvi
dt
= 0
= const.
A"net"upward"
buoyant"force"
on"whatever"fills"
the"hole"
A"net"downward"
force"on"the"
stone"
|Fg| > |Fb|
i.e."accelerate"downward"
“SINK”"
A"net"upward"
force"on"the"
wood"
i.e."accelerate"upward"
“RISE”"
|Fg| < |Fb|
|Fb| = mf g
Archimedes’
principle:
T h e b u oy a n t
f o r c e o n a
s u b m e r g e d
object is equal to
the weight of the
fl u i d t h a t i s
displaced by the
object
p = p0 + ghwhere%
%p0#=%the%pressure%at%the%reference%level,%
%ρ%=%fluid%density%
%h%=%the%depth%of%a%fluid%sample%below%
% % %the%reference%
#p%=%pressure%in%the%sample%
Pressure%varia:on%with%height%and%depth:%
Density(
(uniform)density))
=
M
V
= lim
V 0
m
V
=
dm
dV
=
m
V
For) a) small) volume)
∆V),)measuring)a)mass)
∆m,)the)density)is$
For)a)infinitesimal)volume)dV)with)a)mass)
of)dm,)we)define)a)density)
In)a)case)that)a)material)
is) much) larger) than)
atomic)dimensions,))
GEN 103 General Physics for (Mechanical) Engineering Students
https://www.facebook.com/groups/kmutt.phy103.ME.56/