Measuring anglespeople.physics.tamu.edu/ggp/Teaching/lesson10.pdf · Measuring angles ... 0¡ 45¡...
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Measuring angles ... 0° 45° 90° 180° 50 gon 100 gon 0 gon 0 /4 /2 200 gon degree new degree or gon radian DEG or D GRA or G RAD or R π π
Transcript of Measuring anglespeople.physics.tamu.edu/ggp/Teaching/lesson10.pdf · Measuring angles ... 0¡ 45¡...
Measuring angles ...
0°
45°
90°
180°
50 gon
100 gon
0 g
on 0
/4
/2
200 g
on
degree new degree or gon radian
DEG or D GRA or G RAD or R
!
!
... and calculating arc lengths
0°
45°
90°
180°
0
/4
/2
degree radian
r
!
x"
"
r
!
x"
"
""
x r= #°
2360
$!
" "x r= # !
v v a t
x x v t a t
x v v t
v v a x
= + !
= + ! + !
= + !
= + ! !
0
0 0
2
0
2
0
2
1
2
1
2
2
"
" "
" "
"
( )
Quantities in kinematics
dislocation
velocity
acceleration
! ! " t
# # ! t " t
# ! ! t
! ! " #
= + $
= + $ + $
= + $
= + $ $
0
0 0
2
0
2
0
2
1
2
1
2
2
%
% %
% %
%
( )
Quantities in rotational kinematics
dislocation
velocity
acceleration
angular
angular
angular
The Dictionary
linear rotational how to translate
t t t = t
x ! !r! = r · !!
v = dxdt " = d!
dt v! = r · "
a = dvdt # = d"
dt a! = r · # (*)F $ %$ = %r ! %F
m I I =!
r2 dm
F = dpdt = ma $ = dL
dt = I#
KE = 12mv2 RE
(!)= 12I"2
p = mv L = I" %L = %r ! %p
v = v0 + at " = "0 + #t (**)
x = x0 + v0t + 12at2 ! = !0 + "0t + 1
2#t2 (**)
v2 = v20 + 2a(x" x0) "2 = "2
0 + 2#(! " !0) (**)
(*) valid for drdt = 0
(**) valid for constant a and #
(!)
