Summary LMR - Vertical circular motion

ELOCOT is used here frequently .


3
-C
-




-




-




2 egts
1 FBD

2 LOCOE




Er
am


r
Yo
-

T

mysino my groso


In
tangential direction
Flang mysinO matang
i

= =
.
:

O
a tang gsin
=




ii) In radial direction :
T-mgcoso
= mar


T=

mgcoso
+
m ar
= or wa




cost ↓
go upwards OI
Note : As we
,
of T

↳ tendency to
slang of string
increases .

iii) Tmax
=+ m

Tmin
= -o



Note : Acc .
at
highest pt-> grind
Acc at lowest
pt
+
.

, "just
11

For the
i v) .



particle to
complete VCM.




Minimum speed at Lowest
point
v =

5gL


Minimum speed at halfway point v =

Igh


Minimum speed at
highest point v =

g)




Tlmax-Tmin 3mg
=
Tmax-Tmin
~ =

Gog




~
vii.
For the
particle to
"easily complete" VCM .




speed at Lowest v (n + 4) gl
point
=




speed at halfway point v =
(n + 2 Tg


speed at
highest point v =
ng




viii Tmax-Tmin =

Gog




=
#


= (1) finitea