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8/18/2019 Phys Options
1/4
By Stephanie – [email protected]
Definitions, formulae (most are in the Data Booklet) and
derivations
Option A: M echanics E xtensionA.2.1 Newton’s law
of universal gravitation !"very #o$y in the universe attracts every
other
#o$y with a force that is $irectly proportional to their
masses an$ inversely proportional to
the s%uare of their separation. Between them the force acts
along the line &oining the centres
of the 2 particles.'
2
21
2
21 an$ r
mmG F
r
mm F =∝
A.2.2 (ravitational fiel$ strength the force per unit mass on a
small test mass )$ue to the
gravitational fiel$ of another o#&ect*
A.2.+ an e,pression for the gravitational fiel$ as a function of
$istance from a point mass
2
2
-ismass pointan$masstestwherengravitatiouniversalof laws/Newton0
r
M G
M mm
r
MmG
m
F g
=
==
=
A.2. an e,pression for the gravitational fiel$ at the surface of
a planet
planet-of ra$iusisan$ planetof massiswhereA.2.+/from
2
r mr
mG g p
p
surface =
NB fiel$ strength )at any point* is numerically e%ual to
the acceleration that it pro$uces
A.2.3 gravitational potential energy )of a mass at a point in
space* the wor4 $one in moving
it from infinity to that point
gravitational potential )at a point in space* the wor4 $one
5energy6 per unit mass of a #o$y in
a gravitational fiel$
A.2.7 an e,pression for the escape spee$ of an o#&ect from
the surface of a planet
planet-of surfaceatstrengthfiel$nalgravitatiois/where 2
2
2
1
*)surface*)surface*)*)
energy- potential*an$)4ineticof ion/conservat
2
g r g
r
Gmv
mvr
mmG
E E E E
E E E E
E E E E
p
p
k k p p
kf ki pi pf
kf pf ki pi
=
=
=
∞−=−∞
−=−
+=+
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8/18/2019 Phys Options
2/4
By Stephanie – [email protected]
Definitions, formulae (most are in the Data Booklet) and
derivations
A.+.2 8epler’s thir$ law the s%uare of the perio$ of a
satellite’s or#it is $irectly proportional
to the cu#e of the or#it’s ra$ius )for any close$ or#it*
k T
R RT =∝
2
++2 or
A.+.+ 8epler’s thir$ law
constant1
- perio$
ncecircumferespee$/as
2
spee$-or#italis/where
forcelcentripetaforceattractivenalgravitatio
22
+
2
2
2
2
==
=
=
=
=
=
π
π
GM
T
r
r T
r GM
r vGM
vr
mv
r
MmG
A.+. e,pressions for the 4inetic potential an$ total energy of
an or#iting satellite
r
GMm
r
MmG
r
GMm
r
MmG
r
GM v
r
GMmmv
2
1
2
1 9"8"energytotal
energy potential
A.+.+*-)see/as 2
1
2
1energy4inetic 22
−=−+=+=
−=
===
A..+ coefficient of friction the ratio of the ma,imum frictional
force to the normal reaction
force )acting on an o#&ect* on a particular surface
k fr s fr
F F F F
µ µ =≤ an$
A.:.1 tor%ue )moment of a force* the turning action of a force
a#out an a,isθ τ sin Fr =
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8/18/2019 Phys Options
3/4
By Stephanie – [email protected]
Definitions, formulae (most are in the Data Booklet) and
derivations
Option H: O ptics;.2.2 normal the line at right angles to a
surface
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8/18/2019 Phys Options
4/4
By Stephanie – [email protected]
Definitions, formulae (most are in the Data Booklet) and
derivations
;..+ principal a,is the line $irectly through the mi$$le of the
lens &oining the centres of
curvature of the 2 surfaces
focal point the point on the principal a,is to which light rays
)initially* parallel to the
principle a,is are #rought to focus after passing through
the lens
focal length the $istance #etween the centre of the lens an$ its
focal point
linear magnification the ratio of the sie of the image forme$ #y
the lens to the sie of theo#&ect
o
i
h
hm =
;.:.1 near point the $istance #etween the eye an$ the nearest
o#&ect that can #e #rought into
clear focus )without strain* with the unai$e$ eye ) 2: cm*
far point the $istance #etween the eye an$ the furthest
o#&ect that can #e #rought into clear
focus )without strain* with the unai$e$ eye ) *
;.:.2 angular magnification the ratio #etween the angle that an
o#&ect su#ten$s normally )atthe near point* an$ the angle that
its image su#ten$s as a result of the optical instrument
o
! M θ
θ =
;.:.+ e,pression for angular magnification of a simple
magnifying glass
=or o#&ect of height h an$ $istance d o from
magnifying glass an$ near point N
o
o
o
i
o
i
d
hd
h
M
=
=
≈=θ
θ
θ
θ
tan
tan
Chen image is forme$ at infinity
d o D f f
M =
Chen image is forme$ at near point
Esing thin lens
e%uation f d o
111+=
111 +=
+=
f
f M
;.:.3 e%uation relating angular magnification an$ focal lengths
of the lenses in an
astronomical telescope
=or image #etween o#&ective an$ eyepiece lenses with height
h
e
o
o
e
o
i
o
i
f
f
f
h
f
h
M ==≈=θ
θ
θ
θ
tan
tan
