theto each far a slipping,
the held
with
yo-yo How Determine
yo-yowill is
horizontally string
the m/s. without
each direction
for 2.00 The
Forfriction shown. 2g
rolls 3
of it. =
surface.
what speed pulled around a
magnitude
vertical
acceleration it velocities
sufficient
In If
Misaxle.
right constant
horizontal
yo-yo. wrapped
two mass
the the
F
the
m/s
1.5
VA=
with
is each by linear after atam/s) to have instant.
there horizontally of
attached string downward
a surface cylinder
on for the immediately(Takeg=9.8
disk
restcase
diagram is
figure. this a figure.
the has
at each
what level hollowhandle N309 is
at cylinder
initially held of R in
In free-body thecut,
stringaon rimF m/s
force. B radius
as
stops?thin-walledpoint
a
VB=3
shown. lisin is the vertically,
F
slipping by friction
shown
lengthstring the
yo-yos left
it on and
Fapplied Mand
string.
of
direction
the the before BC acceleration
identical
Draw andas right
? withouta the andpoint falls
mass
? in of the
mass, rodrodtension ramp force andA
m the form
Questions
Subjective
theslipping. mass thethe rolling
points
centre
acceleration
of cylinder in
after
negligible
of thehorizontal cylinder tension
three of 30° the
in the
endmiddle
of Immediately cut.
is
string in slipping,
the
pulled rod is aup roller the that
shows ?rotate
yo-yo free Determine the
without uniform diskroll of uniform
and ShowFind
of thethe constant velocities
is strings Of solid lawn find
the to
Figure
string of it fixed
roll can Due (a) (b)
A (a) (b) (c) A A A
1. 2. 3. 4. 5. 6.
, I. Auniform disc of mass Mand radius Ris
pivoted
Apoint mass mis glued to the disc at its rim, as about the horizontal axis
rest, find the angular velocity of the disc when m shown in figure. If the
reaches
the
through
system its centre
bottom point B 1s released
M
m
B
8. Adisc of radius Rand mass mis
projected on to a horizontal floor with a
that its centre of mass speed is U, and
of o, so that the disc angular velocity is o. What must be the
eventually returns back ?
backward
spin such
9. Aball of mass mand radius r
rolls along a
minimum
value
(0= 0°) of the path is v,. Find the force of circular path of radius R. Its speed at the
the path on the ball as a function of 0.
bottom
R
10. A heavy
homogeneous cylinder has
by a force F, which isappliedmass m and radius R. It is
accelerated
a light drum of radius r through a rope wound around
of static friction is attached to the cylinder (figure). The coefficient
sufficient for the cylinder to roll without slipping.
(a) Find the friction force.
(b) Find the
acceleration a of the centre of the cylinder.
(c) Is it possible to chooser, so
that a is greater than F ? How ?
(d) What is the direction of m
the friction force in the
11. A man pushes a cylinder of circumstances of part (c) ?
shown. There is no slipping at mass m, with the help of a plank of
mass m, as F
force applied by the man is F. any Find:
contact. The horizontal component of the
(a) the acceleration of the
(b) the magnitudes and plank and the centre of mass of the cylinder and
directionsof frictional forces at contact points.
12. For the system shown in
Calculate: (g = 10 m/s) figure, M = 1kg, m = 0.2 kg, r= 0.2 m. M
(a) the linear acceleration of
hoop,
(b) the angular Hoop
acceleration
(c) the tension in the rope.
of the hoop of mass Mand
Smooth
Note Treat hoop as the ring. Assume no
slipping between stringand hoop.
13. A cylinder of mass m is kept
on the
length 12 m, which in turn is kept onedge of a plank of mass 2m and m
7m/s
friction between the plank and the smoothisground. Coefficient of 2m
given an impulse, which imparts it a cylinder 0.1. The cylinder is
velocity. Find the time after which the cylinder velocity 7 m/s but no angular 12m
(g=10 m/s) falls off the plank.
the held
with
yo-yo How Determine
yo-yowill is
horizontally string
the m/s. without
each direction
for 2.00 The
Forfriction shown. 2g
rolls 3
of it. =
surface.
what speed pulled around a
magnitude
vertical
acceleration it velocities
sufficient
In If
Misaxle.
right constant
horizontal
yo-yo. wrapped
two mass
the the
F
the
m/s
1.5
VA=
with
is each by linear after atam/s) to have instant.
there horizontally of
attached string downward
a surface cylinder
on for the immediately(Takeg=9.8
disk
restcase
diagram is
figure. this a figure.
the has
at each
what level hollowhandle N309 is
at cylinder
initially held of R in
In free-body thecut,
stringaon rimF m/s
force. B radius
as
stops?thin-walledpoint
a
VB=3
shown. lisin is the vertically,
F
slipping by friction
shown
lengthstring the
yo-yos left
it on and
Fapplied Mand
string.
of
direction
the the before BC acceleration
identical
Draw andas right
? withouta the andpoint falls
mass
? in of the
mass, rodrodtension ramp force andA
m the form
Questions
Subjective
theslipping. mass thethe rolling
points
centre
acceleration
of cylinder in
after
negligible
of thehorizontal cylinder tension
three of 30° the
in the
endmiddle
of Immediately cut.
is
string in slipping,
the
pulled rod is aup roller the that
shows ?rotate
yo-yo free Determine the
without uniform diskroll of uniform
and ShowFind
of thethe constant velocities
is strings Of solid lawn find
the to
Figure
string of it fixed
roll can Due (a) (b)
A (a) (b) (c) A A A
1. 2. 3. 4. 5. 6.
, I. Auniform disc of mass Mand radius Ris
pivoted
Apoint mass mis glued to the disc at its rim, as about the horizontal axis
rest, find the angular velocity of the disc when m shown in figure. If the
reaches
the
through
system its centre
bottom point B 1s released
M
m
B
8. Adisc of radius Rand mass mis
projected on to a horizontal floor with a
that its centre of mass speed is U, and
of o, so that the disc angular velocity is o. What must be the
eventually returns back ?
backward
spin such
9. Aball of mass mand radius r
rolls along a
minimum
value
(0= 0°) of the path is v,. Find the force of circular path of radius R. Its speed at the
the path on the ball as a function of 0.
bottom
R
10. A heavy
homogeneous cylinder has
by a force F, which isappliedmass m and radius R. It is
accelerated
a light drum of radius r through a rope wound around
of static friction is attached to the cylinder (figure). The coefficient
sufficient for the cylinder to roll without slipping.
(a) Find the friction force.
(b) Find the
acceleration a of the centre of the cylinder.
(c) Is it possible to chooser, so
that a is greater than F ? How ?
(d) What is the direction of m
the friction force in the
11. A man pushes a cylinder of circumstances of part (c) ?
shown. There is no slipping at mass m, with the help of a plank of
mass m, as F
force applied by the man is F. any Find:
contact. The horizontal component of the
(a) the acceleration of the
(b) the magnitudes and plank and the centre of mass of the cylinder and
directionsof frictional forces at contact points.
12. For the system shown in
Calculate: (g = 10 m/s) figure, M = 1kg, m = 0.2 kg, r= 0.2 m. M
(a) the linear acceleration of
hoop,
(b) the angular Hoop
acceleration
(c) the tension in the rope.
of the hoop of mass Mand
Smooth
Note Treat hoop as the ring. Assume no
slipping between stringand hoop.
13. A cylinder of mass m is kept
on the
length 12 m, which in turn is kept onedge of a plank of mass 2m and m
7m/s
friction between the plank and the smoothisground. Coefficient of 2m
given an impulse, which imparts it a cylinder 0.1. The cylinder is
velocity. Find the time after which the cylinder velocity 7 m/s but no angular 12m
(g=10 m/s) falls off the plank.
