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Notes
Course
Description:
Physics is a high school level course
that
satisfies the
Ohio Core
science graduation requirements of Ohio Revised Code Section 3313.603. This section of Ohio law
requires a three

unit course with inquiry

based laboratory experience that engages students in asking valid scientific questions and ga
thering and analyzing information.
Physics elaborates on the study of the key concepts of motion, forces and energy as they relate to increasingly complex syste
ms and applications that will provide a
foundation for further study in science and scientific
literacy.
Students engage in investigations to understand and explain motion, forces and energy in a variety of inquiry and design scen
arios that incorporate scientific reasoning,
analysis, communication skills and real

world applications.
Motion
Graph interpretations
o
Position vs. time
o
Velocity vs. time
o
Acceleration vs. time
In physical science, the concepts of
position, displacement, velocity and
acceleration were introduced, and
straight

line motion involving either
uniform velocity or uniform acceleration
was investigated and represented in
position vs. time graphs, velocit
y vs.
time graphs, motion diagrams and data
tables.
In this course, acceleration vs. time
graphs are introduced, and more
complex graphs are considered that
have both positive and negative
displacement values and involve motion
that occurs in stages (e.g.
, an object
accelerates then moves with constant
velocity). Symbols representing
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Notes
acceleration are added to motion
diagrams and mathematical analysis of
motion becomes increasingly more
complex. Motion must be explored
through investigation and
experimentat
ion. Motion detectors and
computer graphing applications can be
used to collect and organize data.
Computer simulations and video
analysis can be used to analyze motion
with greater precision.
Motion/Graph Interpretations
Instantaneous velocity for an
ac
celerating object can be determined
by calculating the slope of the tangent
line for some specific instant on a
position vs. time graph. Instantaneous
velocity will be the same as average
velocity for conditions of constant
velocity, but this is rarely the
case for
accelerating objects. The position vs.
time graph for objects increasing in
speed will become steeper as they
progress and the position vs. time graph
for objects decreasing in speed will
become less steep.
On a velocity vs. time graph, objects
increasing in speed will slope away from
the x

axis and objects decreasing in
speed will slope toward the x

axis. The
slope of a velocity vs. time graph
indicates the acceleration, so the graph
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Notes
will be a straight line (not necessarily
horizontal) when the
acceleration is
constant. Acceleration is positive for
objects speeding up in a positive
direction or objects slowing down in a
negative direction. Acceleration is
negative for objects slowing down in a
positive direction or speeding up in a
negative direc
tion. These are not
concepts that should be memorized, but
can be developed from analyzing the
definition of acceleration and the
conditions under which acceleration
would have these signs. The word
“deceleration” should not be used since
i琠trovi摥s潮fu
sio渠n整we敮lo睩n朠
摯w渠慮d 条tiv攠ecc敬敲慴eo渮nq桥
慲敡⁵湤敲⁴桥畲v攠e潲ovel潣ity vs⸠
瑩m攠er慰栠hiv敳⁴ e桡ng攠en⁰ si瑩o渠
E摩s灬慣敭敮琩 琠瑨攠e扳潬畴攠e潳i瑩潮
c慮湯琠扥 摥瑥牭i湥搠dr潭 愠a敬潣ity
vs⸠瑩m攠er慰h⸠
l扪散瑳 m潶i湧 睩t栠h湩f
潲o
慣c敬敲慴i潮 will 桡v攠愠a潲iz潮瑡l lin攠
潮渠ncc敬敲慴e潮 vs⸠Kim攠杲慰栮⁔桩s
lin攠睩ll ⁴桥⁸

慸is潲扪散瑳⁴ 慴a
慲攠敩瑨tr瑡湤i湧till爠m潶i湧 睩瑨t
c潮s瑡t琠vel潣ity⸠K桥 慲敡a畮摥r⁴桥
c畲u攠ef 慣c敬敲e瑩o渠vs⸠瑩m攠er慰栠
杩v敳⁴
攠e桡n来 i渠vel潣ity潲⁴桥o
潢j散琬u琠瑨攠eis灬慣敭敮琬⁰潳i瑩o渠
慮搠d桥 慢s潬畴u vel潣ity慮湯琠te
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Notes
determined from an acceleration vs.
time graph. The details about motion
graphs should not be taught as rules to
memorize, but rather as generalizations
that can be developed from interpreting
the graphs.
•
Problem solving
o
Using graphs (average velocity,
instantaneous velocity,
acceleration, displacement,
change in velocity)
o
Uniform acceleration including
free fall (initial velocity, final
velocity, time, displacement,
acceleration, average velocity)
Many problems can be solved from
interpreting graphs and charts as
detailed in the motion graphs section. In
addition, when acc
eleration is constant,
average velocity can be calculated by
taking the average of the initial and final
instantaneous velocities
(
𝒗
𝒂
𝒗
=(
𝒗
−
𝒗
𝒊
)/2
). This relationship
does not hold true when the
acceleration changes. The equation can
be used in conjunction with other
kinematics equations to solve
increasingly complex problems,
including those involving free fall with
negligible air resistance in whi
ch objects
fall with uniform acceleration. Near the
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Notes
surface of Earth, in the absence of other
forces, the acceleration of freely falling
objects is 9.81 m/s
2
. Assessments of
motion problems, including projectile
motion, will not include problems that
requi
re the quadratic equation to solve.
•
Projectiles
o
Independence of horizontal and
vertical motion
o
Problem

solving involving
horizontally launched projectiles
Projectile Motion
When an object has both horizontal and
vertical components of motion, as in a
projectile, the components act
independently of each other. For a
projectile in the absence of air
resistance, this means that horizontally,
the projectile will continue to trave
l at
constant speed just like it would if there
were no vertical motion. Likewise,
vertically the object will accelerate just
as it would without any horizontal
motion. Problem solving will be limited
to solving for the range, time, initial
height, initial
velocity or final velocity of
horizontally launched projectiles with
negligible air resistance. While it is not
inappropriate to explore more complex
projectile problems, it must not be done
at the expense of other parts of the
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curriculum.
Forces, Momentum and Motion
Newton’s laws applied to
com灬數⁰牯 l敭s
Gr慶it慴a潮al潲o攠e湤i敬ds
El慳tic潲o敳
Fric瑩潮潲o敳
s瑡tic湤
ki湥瑩c)
Air敳is瑡湣攠e湤 摲慧d
F潲o敳渠n睯im敮si潮s
o
Adding vector forces
o
Motion down inclines
o
Centripetal forces and
circular motion
䵯m敮瑵tⰠ,m灵ls攠en搠
c潮s敲e慴io渠nfom敮瑵m
Forces, momentum and motion
In earlier grades, Newton’s laws of
m潴o潮⁷敲攠i湴牯摵c敤; 慶i瑡ti潮慬
f潲o敳 搠di敬摳 睥w攠e敳cri扥搠
c潮c数瑵慬ly;⁴ e牡vit慴ao湡l潲o攠
(weight) acting on objects near Earth’s
s畲u慣攠e慳慬cul慴敤㬠;ric瑩潮潲o敳
慮搠摲慧d睥w攠e摤r敳s敤潮c数t
畡lly
慮搠煵a湴nfie搠drom潲o攠ei慧r慭s㬠;湤
f潲o敳敱畩r敤潲irc畬慲am潴o潮⁷敲攠
i湴牯n畣敤o湣数t畡lly⸠䥮 瑨ts潵rs攬e
Newton’s laws of motion are applied to
m慴aem慴ac慬ly敳cri扥n搠dr敤ic琠瑨攠
敦f散瑳f f潲o敳 潲攠o潭灬數
syst敭sf je
c瑳 搠d漠a湡lyz攠
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Notes
objects in free fall that experience
significant air resistance.
Gravitational forces are studied as a
universal phenomenon and gravitational
field strength is quantified. Elastic forces
and a more detailed look at friction are
included
. At the atomic level, “contact”
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扥twe敮⁴桥h慲来a⁰ rticl敳 ⁴ 攠
潢j散瑳⁴ 慴a慰p敡r⁴漠oe⁴ 畣桩n朮g
q桥s攠el散瑲ic潲o敳牥es灯湳ibl攠e潲o
fric瑩潮潲o敳ⰠI潲o慬潲oes 搠d瑨tr
“contact” forces. Air resista
湣攠en搠dra朠
慲攠數灬慩湥d⁵ in朠gh攠e慲瑩cl攠湡t畲攠
潦 m慴a敲⸠er潪散瑩l攠e潴o潮 is湴牯摵ce搠
慮搠dircul慲潴o潮 isⁱ 慮tifi敤⸠K桥
v散瑯爠灲潰敲ei敳 om敮瑵t 搠
im灵ls攠er攠e湴牯n畣敤 慮d⁵ 敤⁴漠
慮alyz攠敬慳瑩c 搠i湥l慳瑩c潬lisi潮s
扥twe敮 潢j
散瑳⸠K湡lysis 潦
數灥rim敮瑡t 摡瑡潬l散瑥d渠
l慢潲慴潲y湶敳瑩g慴a潮s畳琠t攠畳敤
瑯ts瑵ty潲o敳 搠d潭敮瑵t⸠q桩s
c慮湣l畤攠eh攠es攠潦潲oe⁰牯扥s湤
com灵瑥爠t潦瑷慲攠e漠ooll散琠t湤
慮alyz攠摡t愮a
Newton’s laws
Newton’s laws of motion, especially the
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Notes
third law, can be used to solve complex
problems that involve systems of many
objects that move together as one (e.g.,
an Atwood’s machine). The equation
a
=
F
net
/m that was introduced in physical
science can be used
to solve more
complex problems involving systems of
objects and situations involving forces
that must themselves be quantified
(e.g., gravitational forces, elastic forces,
friction forces).
Gravitational Forces and Fields
Gravitational interactions are very weak
compared to other interactions and are
difficult to observe unless one of the
objects is extremely massive (e.g., the
sun, planets, moons). The force law for
gravitational interaction states that the
strength of the
gravitational force is
proportional to the product of the two
masses and inversely proportional to
the square of the distance between the
centers of the masses,
F
g
=
(G∙m
1
∙m
2
)/r
2
)
. The proportionality
constant,
G,
is called the universal
gravitational con
stant. Problem solving
may involve calculating the net force for
an object between two massive objects
(e.g., Earth

moon system, planet

sun
system) or calculating the position of
such an object given the net force.
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Notes
The strength of an object’s (i.e., the
s
ource’s) gravitational field at a certain
l潣慴i潮I
g
, is given by the gravitational
force per unit of mass experienced by
another object placed at that location,
g
=
F
g
/
m
. Comparing this equation to
Newton’s second law can be used to
數灬ai渠睨y 慬l扪
ects on Earth’s
s畲u慣攠ecc敬敲慴攠e琠瑨攠e慭攠牡瑥ei渠
瑨t扳敮c攠潦 r敳is瑡tc攮et桩l攠e桥
杲慶i瑡tio湡l潲o攠erom 潴o敲扪散琠
c慮 畳敤⁴漠o整ermi湥⁴桥i敬搠
s瑲敮杴g 慴a愠灡rtic畬慲al潣a瑩潮Ⱐ瑨攠ei敬搠
潦⁴ 攠e扪散琠is 睡ys 瑨tr攬eev敮f⁴
桥h
潢j散琠ts潴oi湴nr慣ti湧 wit栠hny瑨in朠
敬s攮eq桥i敬搠dir散瑩潮 is⁴ow慲搠a桥
c敮瑥爠潦⁴ 攠eo畲u攮ediven⁴ 攠
杲慶i瑡tio湡li敬d瑲敮杴栠h琠t敲瑡i渠
l潣慴i潮I⁴ e牡vit慴a潮alorc攠e整we敮
瑨t潵rc攠潦⁴ 慴afiel搠慮搠慮y 潢j散琠t琠
瑨t琠l潣慴i潮
c慮攠e慬c畬a瑥t⸠Kr敡瑥爠
杲慶i瑡tio湡li敬d瑲敮杴桳 r敳畬琠t渠
l慲来a 杲慶i瑡瑩o湡l潲o敳 慳s敳
灬慣e搠d渠nh攠ei敬搮ddravit慴a潮ali敬摳
c慮 e灲敳敮t敤 byi敬d a杲慭s
潢瑡i湥搠dy⁰l潴瑩n朠giel搠drr潷s琠t
s敲楥s 潣慴i潮s⸠Kiel搠lin攠e
i慧r慭s
慲攠數clu摥搠dr潭⁴ is潵rs攮e
䑩s瑩湣ti潮s 扥t睥敮 杲gvit慴ao湡l 搠
i湥rtial慳s敳牥 cl畤e搮d
Ac慬攠in摩c慴敳 wei杨ty敡s畲楮朠
瑨t潲o慬潲o攠e整睥敮⁴桥扪散琠t湤
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Notes
the surface supporting it. The reading
on the scale accurately measur
es the
weight if the system is not accelerating
and the net force is zero. However, if
the scale is used in an accelerating
system as in an elevator, the reading on
the scale does not equal
the actual
weight. The scale reading can be
referred to as the
“apparent weight.”
q桩s 灡r敮琠weig桴hi渠ncc敬敲慴in朠
敬ev慴潲o慮攠expl慩湥d 慮搠
c慬c畬a瑥t 畳in朠g潲o攠eia杲慭s 搠
Newton’s laws.
Elastic Forces
Elastic materials stretch or compress in
proportion to the load they support. The
mathematical model for the force that a
linearly elastic object exerts on another
object is
F
elastic
= kΔx,
wh敲攠
Δx
is⁴=e=
摩s灬慣敭敮琠tf⁴=攠e扪散琠tr潭瑳=
r敬慸敤=灯si瑩
o渮nq桥ir散瑩潮=⁴=e=
敬慳tic潲o攠es=睡ys⁴owar搠d桥=
r敬慸敤=灯si瑩o渠nf⁴=e=慳tic=j散琮t
q桥潮s瑡t琠tf⁰牯=潲瑩潮alityⰠ
k,
is the
same for compression and extension
and depends on the “stiffness” of the
敬慳tic j散琮t
Friction Forces
The amount of kinetic friction between
two objects depends on the electric
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forces between the atoms of the two
surfaces sliding past each other. It also
depends upon the magnitude of the
normal force that pushes the two
surfaces together. This can be
repr
esented mathematically as
Fk
=
μk
FN,
where
μk
is⁴=攠e潥f晩ci敮琠tf=
ki湥瑩cric瑩潮⁴=慴a摥p敮摳⁵=o渠nh攠
m慴ari慬s=⁷hic栠h桥⁴睯ws畲u慣敳牥=
m慤攮e
=
S潭整em敳=fric瑩潮潲o敳慮⁰牥ve湴n
潢j散瑳romli摩湧=灡s琠tac栠h瑨trⰠ
敶e渠wh敮=慮=t敲湡l潲o攠es灰lie搠
灡r慬lel⁴=⁴=e⁴w漠o畲u慣敳⁴=慴a慲攠a渠
c潮瑡t琮⁔桩ss慬le搠d瑡ticric瑩潮Ⱐ
睨wc栠is慴a敭慴ac慬ly数r敳敮瑥t=by=
Fs
≤ μs
FN
.
The maxim
um amount of
static friction possible depends on the
types of materials that make up the two
surfaces and the magnitude of the
normal force pushing the objects
together,
Fsmax
= μs
FN
. As long as the
external net force is less than or equal
to the maximum f
orce of static friction,
the objects will not move relative to one
another. In this case, the actual static
friction force acting on the object will be
equal to the net external force acting on
the object, but in the opposite direction.
If the external net
force exceeds the
maximum static friction force for the
object, the objects will move relative to
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Notes
each other and the friction between
them will no longer be static friction, but
will be kinetic friction.
Air Resistance and Drag
Liquids have more drag than gases like
air. When an object pushes on the
particles in a fluid, the fluid particles can
push back on the object according to
Newton’s third law and cause a change
i渠n潴o潮 潦⁴ 攠e扪散琮⁔桩ss 眠
桥lic潰t敲e 灥ri敮c攠li
f琠t湤ow
swimm敲e⁰牯灥l⁴ 敭s敬v敳潲o慲搮a
c潲o敳rom fl畩摳 will 潮ly 扥ⁱ畡湴ifi敤
using Newton’s second law and force
摩a杲慭s⸠
Forces in
T
wo
D
imensions
o
Adding vector forces
o
Motion down inclines
o
Centripetal forces and circular
motion
Net forces will be calculated for force
vectors with directions between 0° and
360° or a certain angle from a reference
(e.g., 37° above the horizontal). Vector
addition can be done with trigonometry
or by drawing scaled diagrams.
Problems can be solved fo
r objects
sliding down inclines. The net force,
final velocity, time, displacement and
acceleration can be calculated. Inclines
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Notes
will either be frictionless or the force of
friction will already be quantified.
Calculations of friction forces down
inclines f
rom the coefficient of friction
and the normal force will not be
addressed in this course.
An object moves at constant speed in a
circular path when there is a constant
net force that is always directed at right
angles to the direction in motion toward
th
e center of the circle. In this case, the
net force causes an acceleration that
shows up as a change in direction. If the
force is removed, the object will
continue in a straight

line path. The
nearly circular orbits of planets and
satellites result from t
he force of gravity.
Centripetal acceleration is directed
toward the center of the circle and can
be calculated by the equation
a
c
= v
2
/r
,
where
v
is the speed of the object and
r
is the radius of the circle. This
expression for acceleration can be
substituted into Newton’s second law to
c慬c畬a瑥tt桥敮瑲ip整el潲o攮epi湣攠eh攠
c敮瑲i灥瑡l潲o攠es n整ef潲o攬ei琠ta渠ne
敱畡瑥t 瑯tfric瑩o渠⡵湢慮k敤畲u敳)Ⱐ
杲慶ityIl慳瑩c潲o
攬e整e⸬Kt漠o敲e潲o
m潲攠oom灬數慬c畬慴i潮sK
Momentum, Impulse and
Conservation of Momentum
Momentum,
p
, is a vector quantity that
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is directly proportional to the mass,
m,
and the velocity,
v
,
of the object.
Momentum is in the same direction the
object is moving and can be
mathematically represented by the
equation
p
= m
v
. The conservation of
linear momentum states that the total
(net) momentum before an interaction in
a closed system is equal t
o the total
momentum after the interaction. In a
closed system, linear momentum is
always conserved for elastic, inelastic
and totally inelastic collisions. While
total energy is conserved for any
collision, in an elastic collision, the
kinetic energy also
is conserved. Given
the initial motions of two objects,
qualitative predictions about the change
in motion of the objects due to a
collision can be made. Problems can be
solved for the initial or final velocities of
objects involved in inelastic and total
ly
inelastic collisions. For assessment
purposes, momentum may be dealt with
in two dimensions conceptually, but
calculations will only be done in one
dimension. Coefficients of restitution are
beyond the scope of this course.
Impulse,
Δ
p
, is the total momentum
transfer into or out of a system. Any
momentum transfer is the result of
interactions with objects outside the
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system and is directly proportional to
both the average net external force
acting on the system,
F
avg
,
and the time
interval of the interaction,
Δt
⸠䥴慮=
m慴aem慴ac慬ly攠牥灲敳e湴n搠by=
Δ
p
=
pf
–
pi
=
F
avg
Δt
⸠.桩s=u慴a潮慮=扥=
畳敤⁴=畳瑩fy=whyom敮瑵t桡湧敳=
摵攠e漠oh攠ex瑥牮慬潲o攠efric瑩潮慮=
扥杮潲敤=睨敮=瑨t=瑩m攠ef湴nr慣瑩o渠
is=t
r敭敬y桯r琮tAv敲慧e潲o攬ei湩tial=
潲i湡l=vel潣ityⰠI慳s爠瑩m攠e湴nrval=
c慮=alc畬慴a搠d渠n畬瑩

s瑥t=睯w搠
灲潢p敭s⸠䙯.=j散瑳⁴=慴a數灥rie湣攠e=
杩v敮=im灵ls攠⡥eⰠI⁴=畣k=comi湧⁴==愠
s瑯t)ⰠI=v慲a整y=潲o支eim攠
com扩湡ti潮s=慲攠a潳si扬攮eqh
攠eim攠
c潵l搠扥m慬lⰠ睨wc栠睯wl搠牥煵ir攠e=
l慲来潲o攠⡥e朮g⁴=攠er畣kr慳桩湧=in瑯t
愠arick⁷all⁴漠o畤d敮瑯瀩⸠
䍯Cv敲e敬yⰠI桥⁴im攠e潵l搠扥=瑥湤e搠
睨wc栠睯wl搠牥dul琠i渠n畣栠hm慬l敲e
f潲o攠⡥eⰠ瑨e⁴牵=k=灬yi湧⁴=攠ere慫s=
f潲潮g⁰=ri潤
=
潦⁴=m攩e
Energy
Gr慶it慴a潮al⁰潴o湴n慬 敮敲gy
E湥rgy i渠n灲i湧s
乵Nl敡r 敮敲ey
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Notes
Work 搠dow敲e
䍯湳敲e慴a潮 潦 敲ey
Energy
In physical science, the role of strong
nuclear forces in radioactive decay, half

lives, fission and fusion,
and
mathematical problem

solving involving
kinetic energy, gravitational potential
energy, energy conservation and work
(when the force and displacement were
in the same direction) were introduced.
In this course, the concept of
gravitational potential ene
rgy is
understood from the perspective of a
field, elastic potential energy is
introduced and quantified, nuclear
processes are explored further, the
concept of mass

energy equivalence is
introduced, the concept of work is
expanded, power is introduced, an
d the
principle of conservation of energy is
applied to increasingly complex
situations. Energy must be explored by
analyzing data gathered in scientific
investigations. Computers and probes
can be used to collect and analyze data
.
Gravitational Potential Energy
When two attracting masses interact,
the kinetic energies of both objects
change but neither is acting as the
energy source or the receiver. Instead,
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Notes
the energy is transferred into or out of
the gravitational field around th
e system
as gravitational potential energy. A
single mass does not have gravitational
potential energy. Only the system of
attracting masses can have gravitational
potential energy. When two masses are
moved farther apart, energy is
transferred into the fi
eld as gravitational
potential energy. When two masses are
moved closer together, gravitational
potential energy is transferred out of the
field.
Energy in Springs
The approximation for the change in the
potential elastic energy of an elastic
object (e.g., a spring) is
ΔE
elastic
= ½ k Δx
2
where
Δx
is⁴=攠
摩s瑡tce⁴=e=慳瑩c扪散琠ts瑲整e桥搠
潲潭灲敳s敤rom瑳敬ax敤e湧t栮h
=
Nuclear Energy
Alpha, beta, gamma and positron
emission each have different properties
and result in different changes to the
nucleus. The identity of new elements
can be predicted for radioisotopes that
undergo alpha or beta decay. During
nuclear interactions, the trans
fer of
energy out of a system is directly
proportional to the change in mass of
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Notes
the system as expressed by
E = mc
2
,
which is known as the equation for
mass

energy equivalence. A very small
loss in mass is accompanied by a
release of a large amount of energ
y. In
nuclear processes such as nuclear
decay, fission and fusion, the mass of
the product is less than the mass of the
original nuclei. The missing mass
appears as energy. This energy can be
calculated for fission and fusion when
given the masses of the p
article(s)
formed and the masses of the particle(s)
that interacted to produce them.
Work and Power
Work can be calculated for situations in
which the force and the displacement
are at angles to one another using the
equation
W =
FΔx
(cosθ)
睨敲攠
W
is the
work,
F
is the force,
Δx
is⁴桥
摩s灬慣敭敮琬湤
θ
is⁴桥=慮gl攠
扥twe敮⁴桥潲o攠en搠dh攠
摩s灬慣敭敮琮⁔桩s=m敡湳⁷桥渠瑨t=
f潲o攠e湤⁴=eis灬慣敭敮t牥=i杨琠
慮gl敳ⰠI漠w潲os=n攠en搠d漠敮敲gy=
is⁴牡湳f敲e敤=t睥w渠nh攠潢j散瑳⸠.畣栠
is=
瑨t慳e潲irc畬慲潴o潮⸠
=
q桥慴a==敲eyh慮g攠潲⁴o慮sf敲s=
c慬le搠dow敲
P
) and can be
mathematically represented by
P = ΔE /
Δt
潲o
P = W / Δt
⸠.o睥ws=ac慬慲a
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property. The unit of power is the watt
(W), which is equivalent to one Joule of
energy transferred in one second (J/s).
Conservation of Energy
The total initial energy of the system
and the energy entering the system are
equal to the total final energy of the
system and the energy leaving the
system. Although the various forms of
energy appear very different, each can
be measured in a way that ma
kes it
possible to keep track of how much of
one form is converted into another.
Situations involving energy
transformations can be represented with
verbal or written descriptions, energy
diagrams and mathematical equations.
Translations can be made betwee
n
these representations.
The conservation of energy principle
applies to any defined system and time
interval within a situation or event in
which there are no nuclear changes that
involve mass

energy equivalency. The
system and time interval may be defin
ed
to focus on one particular aspect of the
event. The defined system and time
interval may then be changed to obtain
information about different aspects of
the same event.
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Notes
Waves
Wave properties
o
Conservation of energy
o
Reflection
o
Refraction
o
Interference
o
Diffraction
Waves
In earlier grades, the electromagnetic
spectrum and basic properties
(wavelength, frequency, amplitude) and
behaviors of waves (absorption,
reflection, transmission, refraction,
interference, diffraction
) were
introduced. In this course, conservation
of energy is applied to waves, and the
measurable properties of waves
(wavelength, frequency, amplitude) are
used to mathematically describe the
behavior of waves (index of refraction,
law of reflection, sing
le

and double

slit
diffraction). The wavelet model of wave
propagation and interactions is not
addressed in this course. Waves must
be explored experimentally in the
laboratory. This may include, but is not
limited to, water waves, waves in
springs, the i
nteraction of light with
mirrors, lenses, barriers with one or two
slits, and diffraction gratings.
Wave properties
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Notes
o
Conservation of energy
o
Reflection
o
Refraction
o
Interference
o
Diffraction
When a wave reaches a barrier or a
new medium, a portion of its energy is
reflected at the boundary and a portion
of the energy passes into the new
medium. Some of the energy that
passes to the new medium may be
absorbed by the medium and
transformed to ot
her forms of energy,
usually thermal energy, and some
continues as a wave in the new
medium. Some of the energy also may
be dissipated, no longer part of the
wave since it has been transformed into
thermal energy or transferred out of the
system due to the
interaction of the
system with surrounding objects.
Usually all of these processes occur
simultaneously, but the total amount of
energy must remain constant.
When waves bounce off barriers
(reflection), the angle at which a wave
approaches the barrier (a
ngle of
incidence) equals the angle at which the
wave reflects off the barrier (angle of
reflection). When a wave travels from a
two

dimensional (e.g., surface water,
seismic waves) or three

dimensional
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(e.g., sound, electromagnetic waves)
medium into anot
her medium in which
the wave travels at a different speed,
both the speed and the wavelength of
the transferred wave change.
Depending on the angle between the
wave and the boundary, the direction of
the wave also can change resulting in
refraction. The am
ount of bending of
waves around barriers or small
openings (diffraction) increases with
decreasing wavelength. When the
wavelength is smaller than the obstacle
or opening, no noticeable diffraction
occurs. Standing waves and
interference patterns between t
wo
sources are included in this topic. As
waves pass through a single or double
slit, diffraction patterns are created with
alternating lines of constructive and
destructive interference. The diffraction
patterns demonstrate predictable
changes as the widt
h of the slit(s),
spacing between the slits and/or the
wavelength of waves passing through
the slits changes.
Light phenomena
o
Ray diagrams (propagation of
light)
o
Law of reflection (equal angles)
o
Snell’s law
o
Diffraction patterns
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Notes
o
Wave
–
灡r瑩cl攠摵慬ity 潦i杨琠
o
Visible spectrum and color
The path of light waves can be
represented with ray diagrams to show
reflection and refraction through
converging lenses, diverging lenses and
plane mirrors. Since light is a wave, the
law of re
flection applies. Snell’s law,
n
1
sinθ
1
= n
2
sinθ
2
, quantifies refraction in
which
n
is the index of refraction of the
medium and
θ
is⁴=攠慮杬e⁴桥=wave=
敮瑥牳爠l敡v敳⁴桥敤iumⰠI桥渠
m敡s畲敤rom⁴=攠e潲m慬i湥.⁔桥=
i湤數=敦r慣瑩潮==m慴ari慬
慮=扥=
c慬c畬a瑥t=by=瑨t=畡ti潮=
n = c/v
,
where
n
is the index of refraction of a
material,
v
is the speed of light through
the material, and
c
is the speed of light
in a vacuum. Diffraction patterns of light
must be addressed, including patterns
from diff
raction gratings.
There are two models of how radiant
energy travels through space at the
speed of light. One model is that the
radiation travels in discrete packets of
energy called photons that are
continuously emitted from an object in
all directions.
The energy of these
photons is directly proportional to the
frequency of the electromagnetic
radiation. This particle

like model is
called the photon model of light energy
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Notes
transfer. A second model is that radiant
energy travels like a wave that spreads
out
in all directions from a source. This
wave

like model is called the
electromagnetic wave model of light
energy transfer. Strong scientific
evidence supports both the particle

like
model and wave

like model. Depending
on the problem scientists are trying t
o
solve, either the particle

like model or
the wave

like model of radiant energy
transfer is used. Students are not
required to know the details of the
evidence that supports either model at
this level.
Humans can only perceive a very
narrow portion of th
e electromagnetic
spectrum. Radiant energy from the sun
or a light bulb filament is a mixture of all
the colors of light (visible light
spectrum). The different colors
correspond to different radiant energies.
When white light hits an object, the
pigments
in the object reflect one or
more colors in all directions and absorb
the other colors.
Electricity and Magnetism
Charging objects (friction,
contact and induction)
Coulomb’s law
Electric fields and electric
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potential energy
DC circuits
o
Ohm’s law
o
Series circuits
o
Parallel circuits
o
Mixed circuits
o
Applying conservation of
charge and energy (junction
and loop rules)
䵡杮整eciel摳湤 敮敲ey
El散瑲潭慧湥tic湴nr慣ti潮s
Electricity and Magnetism
In earlier grades, the following concepts
were addressed: conceptual treatment
of electric and magnetic potential
energy; the relative number of
subatomic particles present in charged
and neutral objects; attraction and
repulsion between electrical charges
and magnetic poles; the concept of
fields to conceptually explain forces at a
distance; the concepts of current,
potential difference (voltage) and
resistance to explain circuits
conceptually; and connections between
electricity and magnetism as observed
in electromagnets, motors and
generators. In this course, the details of
electrical and magnetic forces and
energy are further explored and can be
used as further examples of energy and
forces affecting motion.
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Notes
Charging Objects (friction, contact
and induction)
For all methods of charging neutral
objects, one object/system ends up with
a surplus of positive charge and the
other object/system ends up with the
same amount of surplus of negative
charge. This suppor
ts the law of
conservation of charge that states that
charges cannot be created or
destroyed. Tracing the movement of
electrons for each step in different ways
of charging objects (rubbing together
two neutral materials to charge by
friction; charging by c
ontact and by
induction) can explain the differences
between them. When an electrical
conductor is charged, the charge
“spreads out” over the surface. When an
敬散瑲ical i湳畬慴ar is桡rg敤ⰠI桥
數c敳s爠摥 ici琠tf 散瑲潮s ⁴ 攠
s畲u慣攠es潣慬iz敤⁴
漠om慬l牥愠潦
瑨t i湳畬慴ar⸠
q桥r攠e慮 敬散瑲ic慬 i湴er慣瑩潮s
扥twe敮h慲来a 搠de畴u慬扪散瑳⸠
䵥瑡l潮摵c瑯牳 ve l慴瑩c攠efix敤
灯sitiv敬y桡rg敤整el io湳
surrounded by a “sea” of negatively
c桡r来搠敬散瑲潮s⁴ a琠tlow fr敥ly 睩瑨in
瑨t l慴aic攮e䥦⁴ 攠湥畴牡u 潢j散琠ts m整el
c潮摵c瑯爬⁴桥r敥l散瑲ons渠nh攠
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Notes
metal are attracted toward or repelled
away from the charged object. As a
result, one side of the conductor has an
excess of electrons and the opposite
side has an electron
deficit. This
separation of charges on the neutral
conductor can result in a net attractive
force between the neutral conductor and
the charged object. When a charged
object is near a neutral insulator, the
electron cloud of each insulator atom
shifts pos
ition slightly so it is no longer
centered on the nucleus. The separation
of charge is very small, much less than
the diameter of the atom. Still, this small
separation of charges for billions of
neutral insulator particles can result in a
net attractive f
orce between the neutral
insulator and the charged object.
Coulomb’s law
Tw漠o桡r来搠d扪散瑳Ⱐ睨,c栠hr攠em慬l
com灡r敤⁴ 瑨t 摩s瑡湣攠e整w敥渠
瑨tmⰠ,慮 潤敬e搠ds⁰潩湴桡r来s⸠
T桥潲o敳 瑷e敮⁰潩湴nc桡r来s牥
灲潰潲pi潮慬⁴漠oh攠ero摵c琠
潦⁴ 攠
c桡r来s 搠d湶敲e敬y⁰牯p潲瑩潮慬 瑯t
瑨t煵慲攠潦⁴ eis瑡tc攠扥twe敮⁴桥
灯i湴nc桡rg敳⁛
F
e
= k
e
q
1
q
2
) / r
2
].
Problems may be solved for the electric
force, the amount of charge on one of
the two objects or the distance between
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the two objects. Problems also may be
solved for three

or four

point charges in
a line if the vector sum of the forces is
zero. This can be explored
experimentally through computer
simulations. Electric forces acting within
and between atoms are vastly st
ronger
than the gravitational forces acting
between the atoms. However,
gravitational forces are only attractive
and can accumulate in massive objects
to produce a large and noticeable effect
whereas electric forces are both
attractive and repulsive and te
nd to
cancel each other out.
Electric Fields and Electric Potential
Energy
The strength of the electrical field of a
charged object at a certain location is
given by the electric force per unit
charge experienced by another charged
object placed at that location,
E = F
e
/ q
.
This equation can be used to calculate
the electric fie
ld strength, the electric
force or the electric charge. However,
the electric field is always there, even if
the object is not interacting with
anything else. The direction of the
electric field at a certain location is
parallel to the direction of the ele
ctrical
force on a positively charged object at
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Notes
that location. The electric field caused
by a collection of charges is equal to the
vector sum of the electric fields caused
by the individual charges (superposition
of charge). This topic can be explored
exp
erimentally through computer
simulations. Greater electric field
strengths result in larger electric forces
on electrically charged objects placed in
the field. Electric fields can be
represented by field diagrams obtained
by plotting field arrows at a ser
ies of
locations. Electric field diagrams for a
dipole, two

point charges (both positive,
both negative, one positive and one
negative) and parallel capacitor plates
are included. Field line diagrams are
excluded from this course.
The concept of electric
potential energy
can be understood from the perspective
of an electric field. When two attracting
or repelling charges interact, the kinetic
energies of both objects change but
neither is acting as the energy source or
the receiver. Instead, the energy is
transferred into or out of the electric field
around the system as electric potential
energy. A single charge does not have
electric potential energy. Only the
system of attracting or repelling charges
can have electric potential energy.
When the distance
between the
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attracting or repelling charges changes,
there is a change in the electric potential
energy of the system. When two
opposite charges are moved farther
apart or two like charges are moved
close together, energy is transferred into
the field as e
lectric potential energy.
When two opposite charges are moved
closer together or two like charges are
moved far apart, electric potential
energy is transferred out of the field.
When a charge is transferred from one
object to another, work is required to
s
eparate the positive and negative
charges. If there is no change in kinetic
energy and no energy is transferred out
of the system, the work increases the
electric potential energy of the system.
DC circuits
o
Ohm’s law
o
Series circuits
o
Parallel circuits
o
Mixed circuits
o
Applying conservation of charge
and energy (junction and loop
rules)
Once a circuit is switched on, the
current and potential difference are
experienced almost instantaneously in
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all parts of the circuit even though
the
electrons are only moving at speeds of
a few centimeters per hour in a current

carrying wire. It is the electric field that
travels instantaneously through all parts
of the circuit, moving the electrons that
are already present in the wire. Since
elect
rical charge is conserved, in a
closed system such as a circuit, the
current flowing into a branch point
junction must equal the total current
flowing out of the junction (junction rule).
Resistance is measured in ohms and
has different cumulative effects
when
added to series and parallel circuits.
The potential difference, or voltage
(
ΔV
)ⰠIcr潳s==敲ey潵rc攠es⁴=攠
灯瑥湴n慬=敮敲ey=摩ff敲敮e攠e
ΔE
⤠
s異灬i敤y⁴=攠en敲ey潵rc攠e敲⁵ei琠
c桡r来
q
) (
ΔV = ΔE/q
)⸠.h攠el散瑲ic=
灯瑥湴n慬=摩ff敲敮e攠ecr潳s
=
r敳is瑯爠ts=
瑨t⁰牯摵c琠tf⁴=攠e畲u敮琠a湤⁴=攠
r敳is瑡tc攠e
ΔV = I R
)⸠䥮=灨ysicsⰠInly=
潨mic敳is瑯牳⁷ill=扥瑵摩敤⸠t桥渠
灯瑥湴n慬=摩ff敲敮e攠es⸠.畲u敮琠is⁰=潴oe搠
f潲渠o桭ic敳is瑯爬⁴桥=杲慰栠睩ll攠e=
s瑲慩杨琠li湥=慮d⁴=e⁶慬u攠ef⁴=攠el潰攠
睩
ll攠eh攠牥eis瑡湣攮eSi湣攠en敲ey=is=
c潮s敲ee搠d潲oyl潳e搠do潰ⰠI桥=
敮敲ey⁰畴ui湴n⁴=eys瑥ty⁴桥=
扡瑴try畳琠t煵al⁴=攠en敲gy⁴桡琠is=
瑲慮sf潲m敤y⁴=攠牥eis瑯ts
l潯瀠牵l攩⸠
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High School
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Second
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Third
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Fourth
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Notes
For circuits with resistors in series, this
means that
ΔV
battery
= ΔV
1
+ ΔV
2
+ ΔV
3
+….
q桥慴攠ef=敲ey=瑲a湳f敲
灯w敲e=
慣r潳s=c栠牥his瑯爠ts=敱u慬⁴漠oh攠
灲潤畣琠tf⁴=攠e畲u敮琠t桲潵杨湤⁴桥=
vol瑡t攠ero瀠pcr潳s=c栠h敳is瑯爠t
P =
ΔV I
)=搠
P
battery
= I ΔV
1
+ I ΔV
2
+ I ΔV
3
+… = IΔV
battery.
Equations should be
underst
ood conceptually and used to
calculate the current or potential
difference at different locations of a
parallel, series or mixed circuit.
However, the names of the laws (e.g.,
Ohm’s law, Kirchoff’s loop law) will not
扥 s敳s敤⸠䵥慳畲i湧 搠dn慬yzin朠
捵
rr敮琬⁶潬t慧e 搠牥dis瑡湣攠en
灡r慬lelⰠI敲e敳 搠dix敤irc畩瑳畳琠
扥⁰牯vi摥搮dq桩s慮攠e潮攠睩瑨
瑲慤iti潮慬a扯r慴潲y 敱uipm敮琠t湤
瑨牯畧栠h潭灵瑥爠tim畬慴ao湳⸠
Magnetic Fields and Energy
The direction of the magnetic field at
any point in space is the equilibrium
direction of the north end of a compass
placed at that point. Magnetic fields can
be represented by field diagrams
obtained by plotting field arrows at a
series of locations. Fiel
d line diagrams
are excluded from this course.
Calculations for the magnetic field
strength are not required at this grade
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High School
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Third
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Fourth
Nine Weeks
Notes
level, but it is important to note that
greater magnetic fields result in larger
magnetic forces on magnetic objects or
moving charge
s placed in the field. The
concept of magnetic potential energy
can be understood from the perspective
of a magnetic field. When two attracting
or repelling magnetic poles interact, the
kinetic energies of both objects change
but neither is acting as the e
nergy
source or the receiver. Instead, the
energy is transferred into or out of the
magnetic field around the system as
magnetic potential energy. A single
magnetic pole does not have magnetic
potential energy. Only the system of
attracting or repelling po
les can have
magnetic potential energy. When the
distance between the attracting or
repelling poles changes, there is a
change in the magnetic potential energy
of the system. When two magnetically
attracting objects are moved farther
apart or two magnetica
lly repelling
objects are moved close together,
energy is transferred into the field as
magnetic potential energy. When two
magnetically attracting objects are
moved closer together or two
magnetically repelling objects are
moved far apart, magnetic potent
ial
energy is transferred out of the field.
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igh School
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Fourth
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Notes
Work is required to separate two
magnetically attracting objects. If there
is no change in kinetic energy and no
energy is transferred out of the system,
the work done on the system increases
the magnetic potenti
al energy of the
system. In this course, the concepts of
magnetic fields and magnetic potential
energy will not be addressed
mathematically.
Electromagnetic Interactions
Magnetic forces are very closely related
to electric forces. Even though they
appear to be distinct from each other,
they are thought of as different aspects
of a single electromagnetic force. A flow
of charged particles (including an
electric current) cre
ates a magnetic field
around the moving particles or the
current carrying wire. Motion in a nearby
magnet is evidence of this field. Electric
currents in Earth’s interior give Earth an
數瑥tsiv攠e慧湥tici敬dⰠ睨wc栠is
摥瑥t瑥搠dr潭⁴ 攠eri敮t慴ao渠nf
com
灡ss 敤l敳⸠K桥潴o潮
敬散瑲icallyh慲来a⁰ rticles渠nt潭s
灲潤畣敳慧湥瑩ciel摳⸠啳畡lly 瑨ts攠
m慧湥瑩ci敬摳 i渠n渠nt潭 慲攠a慮d潭ly
潲楥湴敤 慮d⁴ 敲敦潲攠oa湣敬慣栠
潴o敲畴u⁉渠n慧湥瑩c慴ari慬sⰠI桥
s畢慴amic m慧湥瑩ciel摳 慲攠慬ign
敤Ⱐ
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High School
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Notes
adding to give a macroscopic magnetic
field.
A moving charged particle interacts with
a magnetic field. The magnetic force
that acts on a moving charged particle
in a magnetic field is perpendicular to
both the magnetic field and to the
direction of m
otion of the charged
particle. The magnitude of the magnetic
force depends on the speed of the
moving particle, the magnitude of the
charge of the particle, the strength of
the magnetic field, and the angle
between the velocity and the magnetic
field. Ther
e is no magnetic force on a
particle moving parallel to the magnetic
field. Calculations of the magnetic force
acting on moving particles are not
required at this grade level. Moving
charged particles in magnetic fields
typically follow spiral trajectories
since
the force is perpendicular to the motion.
A changing magnetic field creates an
electric field. If a closed conducting
path, such as a wire, is in
the vicinity of a changing magnetic field,
a current may flow through the wire. A
changing magnetic f
ield can be created
in a closed loop of wire if the magnet
and the wire move relative to one
another. This can cause a current to be
induced in the wire. The strength of the
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igh School
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Fourth
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Notes
current depends upon the strength of
the magnetic field, the velocity of the
relat
ive motion and the number of loops
in the wire. Calculations for current
induced in a wire or coil of wire is not
required at this level. A changing
electric field creates a magnetic field
and a changing magnetic field creates
an electric field. Thus, radi
ant energy
travels in electromagnetic waves
produced by changing the motion of
charges or by changing magnetic fields.
Therefore, electromagnetic radiation is a
pattern of changing electric and
magnetic fields that travel at the speed
of light.
The interplay of electric and magnetic
forces is the basis for many modern
technologies that convert mechanical
energy to electrical energy (generators)
or electrical energy to mechanical
energy (electric motors), as well as
devices that produce or receive
electromagnetic waves. Therefore, coils
of wire and magnets are found in many
electronic devices including speakers,
microphones, generators and electric
motors. The interactions between
electricity and magnetism must be
explored in the laboratory setting
.
Experiments with the inner workings of
motors, generators and electromagnets
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igh School
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Notes
must be conducted. Current
technologies using these principles
must be explored.
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