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Uniform and Non Uniform

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A uniform thin cylindrical disk of mass M and radius Ris attached to two identical massless springs of springconstant k which are fixed to the wall as shown in thefigure. The springs are attached to the axle of the disksymmetrically on either side at a distance d from itscentre. The axle is massless and both the springs andthe axle are in a horizontal plane. The unstretched lengthof each spring is L. The disk is initially at its equilibriunmposition with its centre of mass (CM) at a distancefrom the wall. The disk rolls without slipping with velocityVo Voi . The coefficient of friction is u. \lbrack IT-JEE 2008\rbrack

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Q. A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity

_{0} = V_{0}^i

. The coefficient of friction is

μ

.
The maximum value of

V_{0}

for which the disk will roll without slipping is :

Q. A uniform thin cylindrical disk of mass

M

and radius

R

is attached to two identical massless springs of spring constant

k

which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance

d

from its centre. The axle is massless and both the springs and the axle are in horizontal plane. The unstretched length of each spring is

L

. The disk is initally at its equilibrium position with its centre of mass (CM) at a distance

L

from the wall. The disk rolls without slipping with velocity

_{0} = V_{0} ˆ i

. The coefficient of friction is

μ

.
The net external force acting on the disk when its centre of mass is at development

x

with respect to its equilibrium position is

Q. A uniform thin cylindrical disc of mass

M

and radius

R

is attached to two identical massless spring constant

k

which are fixed to the wall as shown in Figure. The springs are attached to the axle of the disk symmetrically on either side at a distance

d

from its centre. The axle is massless and both the springs and the axle are in the horizontal plane. The unstretched length of each spring is

L

. The disc is initially at its equilibrium position with its centre of mass

(C M)

at a distance

L

from the wall. The disc rolls without slipping with velocity

V_{0} = V_{0}^i

. The coefficient of friction is

μ

.
The maximum value of

V_{0}

for which the disc will roll without slipping is :

Comprehension Type: A uniform thin cylindrical disk of mass M ad radius R is attached to two identical mass less springs of springs constant k which are fixed to the wall as show in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its center. The axle is mass less and both the springs and the axle are in horizontal plane. The un-stretched length of each springs is L. The disk is initially at its equilibrium position with its center of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $\to (V)_{0} = V_{0}^i$ The coefficient of friction is $μ$ .

The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is

Q. A disc of mass M and radius R has a spring of constant k attached to its centre, the other end of the spring being fixed to a vertical wall. If the disk rolls without slipping on a level floor, how far to the right does the centre of mass move, if initially the spring was unstretched and the angular speed of the disc was

ω_{o}

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