S.A.T. II: Physics Equation Sheet
Mechanics d t
The trickiest one of all:
v
Average velocity:
v ave =
An equation with v, vo, a, t :
v
=
v o at
An equation with d , vo, a, t :
d
=
v o t at
An equation with v, vo, a, d :
v
Newton's First Law:
!"ects in #otion $or at rest% will stay in #otion $or at rest% unless acted on !y an outside force
Newton's First Law:
Newton's Third Law: Law:
F y
F
(
F x
=
2
F
total displacement total time
1
2
2
=
2
v o 2ad
ma
=
&very force has an equal and oosite force
F x
=
cos F cos
F y = F sin
energy time
Work t
)echanical *ower:
P
+#ulse and )o#entu#:
F t = p = mv final − mv initial
=
=
=
F ⋅v
Frictional Force:
F f = F N
ravitational Force:
F G
-entrietal Force:
.ork done !y centrietal forces:
=
F c
m1 m2
G
2
r
mv r
=
2
Zero!
Force of a sring $/0)%:
F s
= −k
*otential &nergy of a /ring:
PE
*eriod of a *endulu#
T
=
=
1 2
2
x
kx
2
L g
Electrostatics The charge of one electron:
Force !etween 2 charges:
The electrostatic constant k
&lectric field of a oint charge:
0ow are F and E related8
13 4 13516 -
F
=
k
q1 q2 2
r
6 4 13 6 N #7- 2
E
=
k
q 2
r
F q E
q k r
&lectric otential of a oint charge:
"
&lectric otential of a caacitor:
" E d
-aacitance
# $ "
&lectric otential energy slash .ork to #ove a charge:
EPE q %"
=
Circuits h#'s Law:
"&'
2
&lectrical *ower:
P
=
&"
=
2
& '
=
" '
/eries
*arallel
-urrent:
& ( & ) & *
& total & ( + & ) + & *
9oltage:
" total " ( + " ) + " *
" ( " ) " *
esistance:
'total '( + ') + '*
-aacitance:
1
$ total
=
1
$ 1
1
$ 2
1
$ ;
1
'total
=
1
1
1
'1 '2 ';
$ total $ ( + $ ) + $ *
Magnetic Fields & Forces o & 2 '
Field of a /traight .ire:
, =
)agnetic Force on a -harge:
F ,
=
q" ,
)agnetic Force on a .ire:
F ,
=
& l ,
.ork done !y a )agnetic Field:
Zero!
)agnetic Flu4:
< ,-
+nduced 9oltage:
" = emf = −
Len='s Law:
+nduced current generates a #agnetic flu4 that opposes the change in flu4 that induced it
= ,lv t
Modern Physics >ohn ?alton:
esouses the #odern ato#ic theory
> > Tho#son:
discovers the electron $in lu# udding@%
o!ert )illikan:
#easured the charge of an electron
&rnest utherford:
gold foil e4eri#ent $ nuclei, e#ty sace%
Niels Bohr:
electrons in fixed or!its like a solar syste#
.hat is an electron5volt8
1 e9 C 13 4 13516 >
&nergy of light:
E hoton . f
.ork function:
= .f incoming − /E electrons
elativity -orrection Factor:
The ?e5Broglie wavelength:
=
1−
v c
2 2
. p
=
. mv
)oving lengths 8
s.rink!
)oving ti#es 8
r0n slo1er 2longer3!
)oving #asses 8
get .eavier!
Optics c n
/eed of light in a #ediu#:
v
Law of eflection:
1 = 2
/nell's Law of efraction:
n 1 sin 1 = n 2 sin 2
.hich way does light !end8
to1ards the nor#al in a denser #ediu# and a1ay fro# the nor#al in a less dense #ediu#
-ritical angle of internal reflection:
n 1 sin c = n2 sin 63 so
The Lens &quation:
1
f
=
c
sin c =
=
1
d o45ect
n2 n1
1
d image
where f D 3 for converging lenses f E 3 for diverging lenses d i#age D 3 for real i#ages d i#age E 3 for virtual i#ages
)agnification:
m
=
. image .o45ect
= −
d image d o45ect
ay Tracing ules: for lenses
1 one line through the -enter 2 one line arallel to the a4is and through the Focus $; one line through the Focus and then arallel to the a4is%
for mirrors
1 one line through the -enter 2 one line arallel to the a4is and through the Focus $; one line reflected through the oint where the #irror #eets the a4is%
a!es 1
1
Frequency of a wave:
f =
=
/eed of a wave :
v = f
&nergy of a wave:
roortional to $a#litude%2
period
T
?oler shift rules 1 listener and source getting closer
→
frequency goes u $!lue shift%
2 listener and source getting further
→
frequency goes down $red shift%
; listener is #oving
→
seed changes cause freq change
source is #oving
→
G changes cause freq change
Beat frequency:
-onstructive interference ath difference:
?estructive interference ath difference:
f 4eats
=
∣ f − f ∣ 1
2
3, G, 2G, ;G,
2
6
; 2
6
H 2
6
1st har#onic $funda#ental f % of a string:
=
2nd har#onic $1st overtone% of a string:
= L , f 2
nth har#onic of a string:
f n
=
2L ,
n f 1
f 1
=
=
v L
v 2L
= 2 f 1
?ou!le5slit diffraction 1st order #a4i#u# $for slit sacing d and screen distance L%
x =
L d
Ther"al Physics
0eat required to change te#erature
# = m c T
0eat required to change hase:
# = m 7 f
First Law of Ther#odyna#ics:
8 = # − W
/econd Law of Ther#odyna#ics:
or
# = m 7 v
Entropy increases!
+deal as Law:
P "
Boyle's Law:
P 1 " 1
=
P 2 " 2 at constant T, n
-harles' Law:
T 1 " 2
=
T 2 " 1 at constant *, n
.hat does adia!atic #ean8
=
n 'T
No .eat transferred in or o0t!
0ow do we calculate .ork !y a gas8
W = P "
By how #uch does length increase when so#ething is heated8
L = L T for coefficient of linear e4ansion
+deal efficiency:
ideal =
Actual efficiency:
act0al =
T 7ot −T $old T 7ot
Work o0t 7eat in
=
W #in
