10-30 - 17
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Lecture# 24
.
Curved Surfaces and Rolling( cont 'd )
÷; Tw
£t•cno
slip £1. C
Xx#%ftfate V En
In both these scenarios we have VI. =J
To = Exotic =rwe^+
Acceleration -1
-
= .
-
.
-
.
-
s , fr / i
inside of -j| -
1 •
'
curve .
- ;*Eec/-
know that point -oxzj'-
-
0
follows a circular path-
,\
.
of
rhdiusfr.edu#rfIen\Generally \#
I
.
;r r
\ • ai-
/theoierxe.io#en1¥ . -551p=
radius of curve
This gave us Et=( ¥2)£n at A .
Outsideofcurverw¥÷aftertaxaT=rxE€5¥enn=Let's derive as+
= AT + Ex # - wzrtaI×e^n=÷=rx#frw¥en+kkIxtrei)
=( rw)2
- w2( renn )Fr
e^n - rw2e^n
=fIY÷)ei= . ( If)crw÷If the surface is flat EA= - ramen
,
so the outside of a curve tends to lessenaccelerations
.
example :
f(×)=Io # Tw ,-
s * a. ±
TenthiO-
Given :WIIO,tyFind velocities and accelerations of points A$C .
Solution velocities NI =o
slope
:-|FKK - tax =D ffz )= - 1
TIE.
⇐ tafia );en=t'±)
vT=w-xrsI= ( 10k )x( Ft ) ( ftg )
= # G. e) B-
acceleration x= - 1
,WHO ,r= I
have at = - (Pj+w÷)enWe need p : recall the formula f- =
If "Nl
f "lx)= - ± ; -Mzs= . ,
¥45312
as staffed
To get AT =rx E- t TIEN Tt
examine
O.TW
area,fcxtsinkx
#c_kr:B←
to@ Given
A
/\.E=
⇐Ww←
p ¥sWhich of the other points could have velocity -8 ?
@ A
Q B IF To,=Zp twxrpaw
@ C perpendicular
@ none is possible.
to Fa
0Given €1 µfdatn.ie#/
Which of the following could represent the
Ea and ea ?
@ If TEA
@ Is tea
@ ←Ec TEA 15
@ Tea 9€
FEE⇐ io
@w= 10
• C\
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