7

ROTATIONAL
MOTION
Page
1
1 )
The
minute’s
hand
of
a
watch
is
2
cm
long. Find
( a )
the
angular
velocity,
( b )
linear
velocity
and
( c )
the
radial
acceleration.
[ April,
2002 ]
[ Ans:
( a )
π /
1800
rad
/
s,
( b )
π /
900
cm
/
s,
( c )
(
π
2
/
162 )
×
10
−
4
cm
/
s
2
]
( Note:
Linear
velocity
and
radial
acceleration
are
for
a
particle
on
the
tip
of
the
minute’s
hand
of
the
watch. )
2 )
The
length
of
a
simple
pendulum
is
one
metre
and
mass
of
its
bob
is
10
gram.
If
the
angular
displacement
is
36
°
,
find
the angular
acceleration.
[ October,
1998 ]
( Ans:
5.76
rad
/
s
2
)
3 )
A
force
^
^
^
k
j
2
i
2
+
+
=
→
F
is
acting
at
a point
=
→
r
^
^
^
k
j
2
i
2
+
+
away
from
the
axis
of
rotation.
Find
the
torque
acting
on
it.
[ March,
1998 ]
( Ans:
zero )
4 )
The
position
vector of
a
particle
is
=
→
r
^
^
^
k
j
2
i
2
+
+
and
the
force
acting
on
is
.
F
^
^
^
k
7
j
6
i
5
+
+
=
→
Calculate
the
torque
acting
on
the
particle.
[ October,
1997 ]
( Ans:
^
^
^
k
2
j
9
i
8

+
)
5 )
What
should
be
the
maximum
speed
of
a
vehicle
when
it
passes
on
the
inclined
curved
path ?
The
radius
of
the
curved
path
is
200
metre
and
slope
θ
=
11
°
32
‘
.
( The
path
is
frictionless ).
[ March,
1997 ]
( Ans:
20
m
/
s )
( Note:
The
problem
is
incorrectly
framed.
The
path
cannot
be
frictionless.
The
car
cannot
run
on a
frictionless
path.
At
a
very
low
speed,
the
car
will have
a
tendency
to
slide
inwards
on
the
inclined
path
resulting
in
outward
radial
frictional
force
on
its
tyres.
As
the
speed
increases,
this
outward
radial
frictional
force
reduces
and
becomes
zero
at
a
definite
speed.
The
answer
given
is
this
definite
speed
at
which
there
is
no
radial
frictional
force
on
the
tyres
of
the
car
and
which
the author
intends
to
ask.
If
the
speed
of
the
car
increases
further,
car
will have
a
tendency
to
skid
outwards
and
inward
radial
frictional
force
acts
on its
tyres
which
increases
with
speed
of
the
car.
At
a
certain
maximum
speed
of
the
car,
this
frictional
force
reaches
a
maximum value.
If
the
speed
of
the
car
exceeds
this
maximum
value,
it
will skid
outwards,
assuming
that
the
outward
toppling
speed
is
higher than this
speed
which
is
true
for
a
vehicle
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 Spring '06
 Smith
 Acceleration, Friction, Mass, Moment Of Inertia, Velocity, Physical quantities

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