!"#$%&$'()*'+,&-./,'01'
2,3-456$'7"%/8'+93'958':4;<%5='
>4/&,'?/4@;,A$'
:.AA,/':,$$%45'(*'BC(('
'
7",'D.%E'3%;;'&4AA,5&,'9-'F1GG')HI'
J,#'K.,$L45$1'MN%$&.$$'3%-"'5,%="@4/$'
@,O4/,'D.%EP'
(P'Q"9-'%$'9'54/A9;'O4/&,R'
BP'Q"9-'%$'-",'-"%/8';93'?9%/'4O'-",'54/A9;'
O4/&,R'
GP'S43'84'#4.'T543'3",5'$4A,-"%5='%$'9-'
,D.%;%@/%.AR'
UP'Q"9-'"9??,5$'-4'95')-3448'A9&"%5,'
3%-"',D.9;'A9$$,$R'
VP'Q"9-'%$'9'&45-9&-'O4/&,R'
WP'N4'#4.'3,%="'A4/,'=4%5='.?'4/'=4%5='
8435'%5'95'9&&,;,/9L5=',;,<9-4/R ''
X,98%5='K.%E'YVZ('
•  Q"9-'%$'9'54/A9;'O4/&,R'
''
)P  )'O4/&,'-"9-'%$'?,/?,58%&.;9/'-4'-",'A4L45'
[P  ')'O4/&,'-"9-'84,$'54-'5,,8'-4'@,'@/4T,5'.?'%5-4'
&4A?45,5-$''
\P  7",'-"%/8';93'?9%/'4O'-",'O4/&,'4O'=/9<%-#'
NP  )'O4/&,'-"9-'4??4$,$'-",'O4/&,'4O'=/9<%-#'
]P  )'&45-9&-'O4/&,'@,-3,,5'95'4@^,&-'958'-",'
$./O9&,'%-'%$'?;9&,8'45'
'
X,98%5='K.%E'YVZB'
•  Q"9-'%$'-",'-"%/8';93'?9%/'4O'-",'54/A9;'O4/&,R'
''
)P'7",'O4/&,'4O'=/9<%-#'
[P'7",'O4/&,'4O'O/%&L45'
\P'7",'9@54/A9;'O4/&,'
NP'7",'?9/9;;,;'O4/&,'
]P'245,'4O'-",'9@4<,'
X,98%5='K.%E'YVZG'
•  S43'84'#4.'T543'3",5'$4A,-"%5='%$'9-'
,D.%;%@/%.AR'
''
)P'_-'84,$'54-'"9<,'9'O4/&,'45'%-'
[P'_-'84,$'54-'"9<,'9'5,-'O4/&,'45'%-'
\P'7",'$.A'4O'-",'O4/&,$'%5'-",'`'8%/,&L45',D.9;'-",'
$.A'4O'-",'O4/&,$'%5'-",'#'8%/,&L45'
NP'_-'"9$'-"%/8';93'?9%/$'O4/'9;;'4O'%-$'O4/&,$'
]P');;'4O'-",'O4/&,$'45'%-'9/,',D.9;'%5'A9=5%-.8,'
X,98%5='K.%E'YVZU'
•  Q"9-'"9??,5$'-4'95')-3448'A9&"%5,'3%-"',D.9;'
A9$$,$R'
)P  _-'A4<,$'$4'-"9-'-",'A9$$,$'9/,'9-'-",'$9A,'",%="-'
[P  _-'A4<,$'$4'-"9-'-",'A9$$'-"9-'%$';43,/'8435'O9;;$'-4'
-",'=/4.58'
\P  _-'A4<,$'$4'-"9-'-",'A9$$'-"9-'%$'"%=",/'.?'O9;;$'-4'-",'
=/4.58'
NP  _-'84,$'54-'A4<,'
]P  )5')-3448'A9&"%5,'34.;8'5,<,/'"9<,',D.9;'A9$$,$'
X,98%5='K.%E'YVZV'
•  Q"9-'%$'9'&45-9&-'O4/&,R'
''
)P')'O4/&,'@,-3,,5'-34'4@^,&-$'-"9-'9/,'A4<%5='9$'45,'
[P')'O4/&,'@,-3,,5'-34'4@^,&-$'-"9-'9/,'&455,&-,8'@#'9'
/4?,'
\P')'O4/&,'@,-3,,5'-34'4@^,&-$'-"9-'9/,'?.;;%5='45',9&"'
4-",/'
NP')'O4/&,'@,-3,,5'-34'4@^,&-$'-"9-'9/,'?.$"%5='45',9&"'
4-",/'
]P'245,'4O'-",'9@4<,'
X,98%5='K.%E'YVZW'
•  N4'#4.'3,%="'A4/,'=4%5='.?'4/'=4%5='8435'%5'95'
9&&,;,/9L5=',;,<9-4/R'
''
)P'a4%5='.?'
[P'a4%5='8435'
\P'7",#'9/,',D.9;'
NP'_-'8,?,58$'45'3",-",/'#4.'9/,'$?,,8%5='.?'4/'
$;43%5='8435'
'
'
)554.5&,A,5-$'
•  \",&T'=/98,'O4/'>%/$-'K.%E'45;%5,'
•  7"/,,'4b&,'"4./$c'M%5'H9#,/'S9;;'VWBGP'
–  HdQ'O/4A'(BZ(?A'
–  7.,$'O/4A'VZW?A'
•  S4A,34/T'YG'%$'?4$-,8*'8.,'Q,85,$89#'
•  ]`-/9'?/4@;,A$'9/,'?4$-,8'M9;$4'$4;.L45$'-4',<,5'
5.A@,/,8'?/4@;,A$P'
•  \;%&T,/'=/98,$'3%;;'@,'.?'$445'''
•  !%&T'.?'4;8'"4A,34/T'O/4A'A,'%5'4b&,'"4./$'4/'
-4A4//43'
)554.5&,A,5-$'
[4.589/%,$'O4/'e59;'
=/98,$'M&4.;8'=4';43,/'
@.-'54-'"%=",/P1'
• 
• 
• 
• 
ffg'O4/'95')'
0Vg'O4/'9'['
WBg'O4/'9'\'
VCg'O4/'9'N'
+4-$'4O'4??4/-.5%L,$'-4'
%A?/4<,'=/98,1'
'
•  N/4?';43,$-'K.%E'
•  N/4?';43,$-'S4A,34/T'
•  N/4?';43,$-'U'4.-'4O'(U'
X,98%5='K.%EE,$'
•  734'9;-,/59-,'/.@/%&$'
•  h?'-4'Vg',`-/9'&/,8%-'
O4/'\;%&T,/$'
)545#A4.$'?4;;'
N4'#4.'?/,O,/'-4'$-.8#'3%-"'-",'-,`-@44T'?/4@;,A$'4/'-",'
34/T$",,-'?/4@;,A$R'
''
)P'7",'-,`-@44T'%$'@,i,/I'
[P'7",'34/T$",,-$'9/,'@,i,/I'
\P'_';%T,'@4-"'4O'-",A*'%-6$'=448'-4'"9<,'9';4-'4O'?/9&L&,I'
NP'_'8456-';%T,',%-",/'4O'-",A*'958'#4.6/,'9$T%5='.$'-4'84'
-44'A.&"I'
]P'_'8456-'-"%5T',%-",/'9$$%=5A,5-'",;?,8'A,'?/,?9/,'O4/'
-",'e/$-'K.%EI'
\;%&T,/'D.,$L45'0Z('
•  )'$-,,;'@9;;'%$'9i9&",8'-4'9'
$-/%5='958'%$'$3.5='%5'9'
&%/&.;9/'?9-"'%5'9'"4/%E45-9;'
?;95,'9$'%;;.$-/9-,8'%5'-",'
e=./,I'')-'-",'?4%5-'!'-",'
$-/%5='$.88,5;#'@/,9T$'5,9/'
-",'@9;;'I''_O'-",$,',<,5-$'9/,'
4@$,/<,8'O/4A'8%/,&-;#'9@4<,'
9$'%5'-",'e=./,*'3"%&"'?9-"'
34.;8'-",'@9;;'A4$-'&;4$,;#'
O4;;43'9j,/'-",'$-/%5='
@/,9T$R'
\;%&T,/'D.,$L45'0ZB'
•  Q"%&"'4O'-",'O4;;43%5='$-9-,A,5-$'%$'&4//,&-R'
)P  )'E,/4'5,-'O4/&,'%A?;%,$'-"9-'95'4@^,&-'3%;;'
&4A,'-4'/,$-'
[P  )'545E,/4'5,-'O4/&,'45'95'4@^,&-'%A?;%,$'-"9-'%-'
3%;;'A4<,''
\P')5'4@^,&-'9-'/,$-'&4.;8'"9<,'9'545E,/4'5,-'O4/&,'
NP')5'4@^,&-'%5'A4L45'A.$-'"9<,'9'5,-'O4/&,'45'%-'
]P'245,'4O'-",'9@4<,'
\;%&T,/'D.,$L45'0ZG'
•  )'k#'&4;;%8,$'3%-"'9'3%58$"%,;8I''Q"%&"'O4/&,'%$'
=/,9-,/'%5'A9=5%-.8,R'
)P  7",'O4/&,'-",'k#',`,/-$'45'-",'3%58$"%,;8'
[P  7",'O4/&,'-",'3%58$"%,;8',`,/-$'45'-",'k#'
\P''7",'-34'O4/&,$'9/,',D.9;'
2,3-456$'>%/$-'+93'
An object continues in a state of rest or
in a state of motion at a constant speed
along a straight line, unless compelled to
change that state by a net force.
-which means-
An object does not need need to be under
the influence of a force to be in motion!
2,3-456$':,&458'+93'
A net force (ΣF) on an object of mass
(m) results in an acceleration (a)
according to the following formula:
ΣF=ma
2,3-456$'7"%/8'+93'
If two object interact, the force exerted by object 1
on 2 is equal in magnitude and opposite in
direction to the force exerted by object 2 on 1 :
F12= -F21
-In other words-
For every action there is an equal and opposite
reaction.
2,3-456$'7"%/8'+93'
\'
\45&,?-'
•  );;'O4/&,$'4@,#'2,3-456$'7"%/8'+931'
>4/&,'45'@4`''
@#'=/4.58'
>4/&,'45'@4`''Fn
@#'A95'
Fp
A!
>4/&,'45'A95'
@#'@4`'
>4/&,'45'@4`''
@#'O/%&L45'
Fp
Ff
Fg
>4/&,'45'@4`''
@#']9/-"'
N4'>lA9''
45'45,'4@^,&-''
9-'9'LA,c''
>4/&,'45''
]9/-"'@#''
@4`'
>4/&,'4O''
O/%&L45'45'
=/4.58'
Fg
Ff
Fn
Q,%="-'4O'
@4`'45'
=/4.58'
\;%&T,/'K.,$L45'0ZU'
!"#$%&'()*)+,-.&+%/*
Q"9-'"9??,5$'3",5'95'4@^,&-',`,/-$'9'O4/&,'45'
%-$,;OR'
'
)P  _-'3%;;'A4<,'%5'-",''
8%/,&L45'4O'-",'O4/&,'
[P'''_-'3%;;'$-958'$L;;''
7",'54/A9;'O4/&,'
\'
\45&,?-'
•  _5'A9-",A9L&$'m54/A9;n'958'm?,/?,58%&.;9/n'
9/,'$#545#A$I'
!'7",'54/A9;'O4/&,'%$'9;39#$'?,/?,58%&.;9/'-4'-",'
$./O9&,'%-'%$'%5'&45-9&-'3%-"I'
F
Fn
>4/&,'45'@4`''
@#'=/4.58'
n
>4/&,'45'@4`''
@#'=/4.58'
A!
o'
\;%&T,/'K.,$L45'0ZV'
)'@4`'%$'@,%5='?.$",8'.?'9=9%5$-'9'39;;I''Q"%&"'
<,&-4/'$"43$'-",'8%/,&L45'-"9-'-",'"#$%&''O4/&,'
%$'?4%5L5=R'
'
)P'
[P'
Fn
Fn
NP'
Fn
]P'
Fn
\P'
Fn
A!
N/93%5='>/,,''
[48#'N%9=/9A$'
•  N/93'9'?%&-./,'3%-"'9'
&44/8%59-,'$#$-,A'
M/,?/,$,5-'4@^,&-'9$'
?4%5-'A9$$P'
•  N/93'9//43$'=4%5='939#'
O/4A'-",'4@^,&-'-4'
/,?/,$,5-'-",'O4/&,$*'
;9@,;'-",A'
•  7/#'-4'A9T,';,5=-"'4O'
9//43'&4//,$?458'-4'
$-/,5=-"'4O'O4/&,'
•  [/,9T'.?'%5-4'
&4A?45,5-$'%O'5,&,$$9/#'
'
!'
!/4&,8./,'
T o' T cos θ
T sin θ
Fg
#'
`'
\;%&T,/'D.,$L45'0Z('
•  Q"%&"'4O'-",$,'%$'?/4@9@;#'54-'%5',D.%;%@/%.AR'
D)
C)
A)
B)
!/9&L&,'8/93%5='>[N$'
•  p4.'?.$"'9'@44T'
•  )'/4?,'?.;;$'95'
8435'<,/L&9;;#'45'9' ,;,<9-4/'.?'9-'9'
-9@;,'
&45$-95-'<,;4&%-#'
FN
FP
Fg
T
Fg
!/9&L&,'8/93%5='>[N$'
•  )'@4`'$;%8,$'8435'9' •  p4.'@4.5&,'9'@9;;'4q'
O/%&L45;,$$'/9A?'
4O'9'39;;'
FN
Fb
Fg
Fg
o'
!/9&L&,'8/93%5='>[N$'
•  p4.'?.$"'9'@4`'-"9-'
?.$",$'954-",/'@4`'
45'9'O/%&L45;,$$'
$./O9&,'
A('
FN 1
F21
FN 2
FP
A('
Fg1
AB'
AB'
Fg2
F12
[/,9T%5='.?'O4/&,$'%5-4''
&4A?45,5-$'45'95'%5&;%5,'
!'
!/4&,8./,'
Fg sin θ
Fg
Fg
o'
o'
Fg cos θ
[/,9T%5='.?'O4/&,$'%5-4''
&4A?45,5-$'45'95'%5&;%5,'
!'
!/4&,8./,'
#'
`'
FN
FN
o'
o'
FN sin θ
FN cos θ
\;%&T,/'K.,$L45'0Z'
&4A?45,5-$'45'95'%5&;%5,'
A)
A cos θ
A sin θ
o'
A
A
A cos θ
A sin θ
o'
B)
D)
A
C)
A cos θ
A sin θ
o'
A
o'
A cos θ
A sin θ
o'
A
a%<,5'&9.$,'4O'A4L45*'?/,8%&-'%-c'
•  S43';45='3%;;'%-'-9T,'-4'?.$"'-34'@;4&T$'9'
8%$-95&,'(!%O'#4.'?.$"'45'@;4&T'('3%-"')*R'
FN 1
F21
FN 2
FP
A('
AB'
Fg2
Fg1
�
Fx1 = FP − F21 = m1 a
F12
�
Fx2 = F12 = m2 a
a%<,5'&9.$,'4O'A4L45*'?/,8%&-'%-c'
•  S43';45='3%;;'%-'-9T,'-4'?.$"'-34'@;4&T$'9'
8%$-95&,'(!%O'#4.'?.$"'45'@;4&T'('3%-"')*R'
�
Fx1 = FP − F21 = m1 a
1 2
�
d = at
Fx2 = F12 = m2 a
2
�
|F12 | = |F21 |
FP = (m1 + m2 )a
FP
a=
(m1 + m2 )
t=
t=
�
2d
a
2d(m1 + m2 )
FP
S4A,34/T'
•  X,98%5='D.%E'-4A4//43'
•  S4A,34/T'YG'%$'?4$-,8*'8.,'Q,85,$89#'
•  ]`-/9'?/4@;,A$'9/,'?4$-,8'M9;$4'$4;.L45$'-4'
,<,5'5.A@,/,8'?/4@;,A$P'
•  rb&,'"4./$'-489#'9-'5445*'9$T'9@4.-'-",'e/$-'
K.%EI'