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Rotational Motion:
Physics
Q.1) Circular dise of mass 2 Kg and radius 1 m is rotating about an axis perpendicular to its plane and passing
through its centre of mass with a rotational kinetic energy og 8 J. The angular momentum in (J — sec) is
[Als
Q.2) A disc is rolling (without slipping) on a horizontal surface. C is its centre and Q and P are two points
equidistant from C. Let Vp, Vqand V, be the magnitude of velocities of points P, Q and C respectively, then
TAVy > Ve > Vp
(BV < Ve
m
Q.3) As shown in the figure, a bob of mass m is tied to a massless string whose other end portion is wound on a fly
wheel (disc) of radius r and mass m_. When released from rest the bob starts falling vertically. When it has covered a
distance of h, the angular speed of the wheel will be:
wis DIY a
Q.4) The wheels on the old-time bicycle shown in the diagram have radii of 60.0 cm. and 10.0 cm. If the larger
wheel is rotating at 12.0 rad s~!_, what is the angular speed of the smaller wheel?
[A] 12.0 rad s™
[B] 60.0 rads“!
(C] 72.0 rad s
[D] 2.0 rad s“!
Q.5) The rotational analogue of force in linear motion is :
[A] Torque
[B] Weight
[C] Moment of inertia
[D] Angular momentum
Q.6) For increasing the angular velocity of an object by 10%, the kinetic energy has to be increase by
[A] 40%
[B] 20%
[Cc] 10%
[1D] 21%
Q.7) A dancer is spinning on a rotating table with his arms extended, if he folds his arms then the angular velocity
will:
[A] Increase [B] Decrease
[C] Remain unchanged
[D] None of the Above
Q.8) A flywheel is making 300 rpm, Its angular velocity in radian per second is,
[A] 5
[B] sx
[C] 10%
[D] More than one of the above
Q.9) A wheel has angular acceleration of 3 rad/s? and an initial angular speed of 2 rad/s. In a time of two second it
has rotated through an angle (in radians) of
[A] 10
[B] 12
Q.10) A wheel 0.5m in radius is moving with speed of 12m/s. Find its angular speed,
[A] 26 rad/s
[B] 20 radis
[C] 24 rad/s
[D] 22 rad/s
Q.11) What is the moment of interia of a sphere of mass 20 Kg and radius + m about its diameter?
[A] 0.20 Kem?
[B] 0.5 Kem?
[C] 0.10 Kem?
[D] 0.15 Kem?
Q.12) Find the expression for radius of gyration of a solid sphere about one of its
tay 2R =
2
water
Fo
3
vel
7
Q.13) The angle 0 covered by a body in rotational motion is given by the equation 0 = 6t + St? + 2t3
Determine the value of instantaneous angular velocity and angular acceleration. At time t = 2s.
[A] 36 rad/s?
[B] 30 rad/s?
[C] 34 rad/s?
[D] 32 rad/s*
Q.14) A solid cylinder of mass 20kg rotates about its axis with angular speed 100 radisee. ‘The radius of the eylinder
is 0.25m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular
‘momentum of the cylinder about its axis?
[A] 63 Js
[B] 60.5 Is
[c] 623s
[D] 62.5 Js
Q.15) Linear velocities of all the particles of the body in rotational motion is,
[A] Same
[B] Different
Q.16) The combination of rotational motion and the translational motion of a rigid body is known as
[A] Frictional motion
[B] Axis motion
[C] Angular motion
[D] Rolling motion
Q.17) A solid sphere is rotating in free space. Ifthe radius of the sphere is increased keeping mass same, which one
of the following will not be affected? [A] Moment of inertia
[B] Angular momentum
[C] Angular velocity
[D] Rotational kinetic energy
Q.18) The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is I. It
is rotating with angular velocity @. Another identical ring is gently placed on it so that their centres coincide. If both
the rings are rotating about the same axis then loss in kinetic energy is
Q.19) A disc is rotating with an angular velocity @y. A constant retarding torque is applied on it to stop the dise. The
Ic .
angular velocity becomes “S* after n rotations, How many more rotations will it make before coming to rest ?
[Ala
Q.20) Consider a body, shown in figure, consisting of two identical balls, each of mass M_ connected by a light rigid
rod, If an impulse J = MV _ is imparted to the body at one of its ends, what would be its angular velocity ?” Rotational Motion:
Explanations:
Physics
Q.1) Explanation:
KER
Q.2) Explanation:
In case of pure rolling bottom most point is the instantaneous centre of zero velocity.
Velocity of any point on the dise, V = ra , where ris the distance of point from the centre. Since the
distances of these points from the centre are in the order.
1Q>rC>rP_ Hence, the velocities of these points are also in the same order
‘Therefore, the correct option is (1).
Q3) Explanation:
Using work-energy theorem
inv? + He?
v? + Lo
mgh
mgh =4mo?r? +4 6 (sincel = ™ and v=ro
2°2
2
mgh = 3mor
ae
Hence, @ = V =
Q4) Explanation:
‘The linear velocity of both wheels will be the same
60%12=10x0
o=72 rads!
Q.5) Explanation: The rotational analogue of force in linear motion is torque,
> o>
Rotational Analogue of force in linear motion is torque. T = r * F Force is necessary for a body to
do translational motion. Similarly it is the torque which is required to rotate a body. If net torque applied on
the body about the axis of rotation is zero, then the body does not rotate.
Q.6) Explanation:
Let initial energy be K and angular velocity be W after change become K’ and w’
@ =1.1@ (given)
Lig?
K = He’
K'=41@y
$1.10)?
= 1.21(310?)
=121K
Therefore, Kinetic energy should be increased by 21%
Q.7) Explanation:
‘The angular momentum of a body is given as,
=L=lo
If the angular momentum is constant, then,
=o «+ 4”)
T
« Since there is no external torque is acting on the dancer, so his angular momentum will remain to
conserve when he folds his arms.
+ When the dancer folds his arms his moment of inertia decreases so the angular velocity increases.
Hence, option 1 is correct.
Q.8) Explanation:
Given data,
revolutions
0 minute
Flywheel making 301
Using the concept of,
Revolution = 27 Radians and,
1 min = 60 seconds + 300
rev y 1 min
x A min
min ™ 60
Now Angular velocity of flywheel is ©
fad
3 o=5 x Int
= 10m 8
Q.9) Explanation
Given:
a = 3rad/s?, «0, = 2rad/s, t =
We know that,
O= cpt + fat?
O=(2x2)+4 x3x2?
0=4+6=10 radians
Q.10) Explanation:
Angular speed can be given as V =r
aya
SOT as
= 0 = 24rad/s
Q.11) Explanation:
I MR?
1=2x20x(4)?
1=0.5Kgm?
Q.12) Explanation:
Moment of interia of a solid sphere about its diameter can be given as
2p?
=3 ‘MR’
K = Radius of Gyration
1=MK? = 2MR? Q.13) Explanation
Given;
= 614507 +213
Now, Angular velocity @ = 2 = 6 + 10t + 6t?
Att=2s
=6 + 10(2) + 6(2)?
=> = 50 rad/sec
Again, angular acceleration can be given as,
a= 22 = £8 = 19412
dt dt?
Att=2s
a=10+12(2)
a= 34 rad/s
Q.14) Explanation:
Mass of the cylinder is given as, m= 20Kg
Angular speed is given as, @ = 100rad/s
Radius of the cylinder, r= 0.25 m
The moment of interia of the solid cylinder can be given as:
1s
Now,
=1=4%20% (0.25)
=> 1 = 0.625 kgm?
Kinetic energy can be given as : K.
= K.E.= 4 x 6.25 x (100)? = 3125]
Angular momentum can be given as, L=lo
=> L=6.25 x 100
=>L=62.5Js
Q.15) Explanation
In rotational motion, linear velocities of all the particles of the body are different,
Q.16) Explanation
The rolling motion is a combination of translational motion and rotational motion.
Q.17) Explanation:
Angular momentum (L) is the product of the moment of inertia (I) and the angular velocity («),
represented by the equation L =I x
If the mass of the solid sphere remains the same and only the radius is increased, the moment of inertia (1)
will change.
However, according to the conservation of angular momentum, if no external torques are acting on the
system, the angular momentum remains constant.
So, when the radius is increased, the moment of inertia will increase, but the angular velocity will decrease in
such a way that the product (angular momentum) remains constant.
‘Therefore, the angular momentum will not be affected by the change in radius.
Q.18) Explanation
From conservation of angular momentum
To, = loz
Rightarrow Io = 210;
> mas
ay2a
New KE = 48) 7 =!
Loss in KE = Jo? = I = Ie
Q.19) Explanation
Retarding torque is constant. Therefore, angular retardation say 0. will also be constant. applying
2 = oe
oF = 2-200 we get,
(2)? =o = 208)
and 0 = (%) = 200)
Solving n and 2n, we get
Therefore, the dise will make \fiac{n} {3} more rotation before coming to rest.
Q.20) Explanation:
Given Mass of each ball = M .
Impulse applied J = MV
Let the impulse J acts for a small time interval At ,
L
<4
M CCM) M
_——_—_——_*
ai
Then by def. of impulse, J = mv
Mv
= Pa
= The force applied
‘Torque on the system (rod and two balls) about the centre of mass,
Lo ML
tem =F X= Ree
Change in angular momentum,
AL = My. Lx jp MeL @
‘The change in angular momentum ,
AL=Ly -Li
AL = Tomo = [M(E)7+M(4)"Jo
= 5MLe ...Gi)
From equations (i) and (ii) we get,
vL.
2
So=h.
IMLo =
IML =
Hence the angular velocity Rotational Motion:
Answers:
Physics
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