81.
It is easier
to revolve a stone by attaching it to shorter string rather than
to a longer one. Why?
In
rotational dynamics, the torque required for revolution is
defined as the product of the moment of inertia (I) and
angular acceleration
(a)
i.e.
t
=
Ia
=ml^{2}a.
Here,
m is the mass of stone an l is the length of string. When
the string is shorter i.e. l will be smaller then less
torque is required to revolve. hence, it is easier to
revolve a stone by attaching it to shorter string rather
than to a longer one.
82. The
moment of inertia of two rotating bodies are I_{1}
and I_{2}
(I_{1}>I_{2})
and equal angular momentum. Which one has greater K.E.?
The moment
of inertia
of two
rotating
bodies are I_{1}
and I_{2 }
(I_{1}>I_{2})
and equal
angular
momentum
i.e. L_{1}
= L_{2}
= L (say).
The kinetic
energy K.E.
of the
rotating
body is
given by the
relation:
Where,
w
is the angular velocity of the rotating body.
For the same angular momentum, the ratio of kinetic energy
of first rotating body to the kinetic energy of second body
is equal to the ratio of their respective reciprocal moment
of inertias. As
I_{1}>I_{2
} so, Kinetic energy of the second body is greater then
that of the first body.
83. In a
flywheel, most of the mass is concentrated at the rim. Why?
In a
flywheel, the most concentration of mass at the rim
increases moment of inertia (I) of the wheel. Greater the
moment of inertia, greater will be the opposition to the
rotating motion. Hence, such a flywheel helps in maintaining
uniform rotation. If a flywheel of large moment of inertia
is used in the machine, it runs smoother & steadier. Hence,
most of the mass is concentrated at the rim in a flywheel.
84. Two
satellite of equal mass are orbiting the earth at different
height. Considering them as particles, do they have equal moment
of inertia?
Two
satellite of equal mass are orbiting the earth at different
height. Considering them as particles, they usually don't
have equal moment of inertia. The moment of inertia (I) will
be different if two satellites of equal mass are orbiting
the earth at different height as the distance from the axis
of rotation varies as
For
the satellite revolving at a greater height, distance from
the axis of rotation is large so, it will have greater
moment of inertia than other revolving at lower height.
85. A planet
revolves round the sun in a high elliptical orbit. Is its
angular momentum constant over the entire orbit?
A planet
revolves round the sun in a high elliptical orbit. Yes, the
angular momentum L of the planet is constant over the
entire orbit. This is because the revolution of planet round
the sun is due to gravitational force, which is a radical
force, and the torque is zero. According to principle of
conservation of angular momentum, "in the absence of
external torque, the total angular momentum of the system
remains conserved" i.e. L = I
w
= constant (where I is moment of inertia &
w
be the angular velocity). Hence, the angular momentum L is
conserved whatever be the nature of orbit.
86. If no
external torque acts, will the angular velocity remain constant?
According
to principle of conservation of angular momentum, "in the
absence of external torque, the total angular momentum L of
the system remains conserved" i.e. L = I
w
= constant (where I is moment of inertia &
w
be the angular velocity). If one of the parameter (i.e. I or
w)
increases then other decreases and viceversa in order to
conserve angular momentum. So, the angular velocity
w
will remain constant as long as moment of inertia I remains
constant from the principle of conservation of angular
momentum.
87. How does a ballet dancer take
advantage of the principle of conservation of angular momentum?
According
to principle of conservation of angular momentum, "in the
absence of external torque, the total angular momentum of
the system remains conserved" i.e. L = I
w
= constant (where I is moment of inertia &
w
be the angular velocity). During the course of the
performance of a ballet dancer, when the ballet dancer
stretches his or her arms or legs, his or her moment of
inertia increases. As a result, his or her angular velocity
w
decreases such that angular momentum L remains conserved.
When the ballet dancer wants to increase the spinning rate
i.e. angular velocity
w
then he or she has to decrease moment of inertia (I). He or
she has to bring his or her arms & legs closer to decrease
I. In this way, ballet dancer take advantage of the
principle of conservation of angular momentum.
88. The speed
of a whirlwind in a tornado is very high. Why?
In a
whirlwind, air from very near region will concentrate in a
small space. As a result, moment of inertia I will be
decreased. As every system will try to keep the angular
momentum L conserved in absence of external torque i.e. L =
I
w
= constant (where I is moment of inertia &
w
be the angular velocity). If moment of inertia decreases
then the angular velocity
w
must be increased to a high value in absence of external
torque. Hence, the speed of a whirlwind in a tornado is very
high.
89. If the
ice on the polar caps of the earth melts, how will it affect the
duration of day?
Earth
rotates on its own axis from west to east. When ice melts the
mass concentrated near the axis of rotation will spread out.
Hence, moment of inertia I increases. In the absence of external
torque, the angular momentum of the system remains conserved
i.e. L = I
w
= constant (where I is moment of inertia,
w
be the angular velocity & T be the time period).
To remain angular momentum L constant, when moment of
inertia I increase, its angular velocity has to be decreased
which increases the time period T. Hence, the length
or duration of the day will be increased if the ice on the
polar caps of the earth melts.
90. How is a
cat able to land on its feet after a fall?
While
falling, a cat stretches its body along with the tail. Its
moment of inertia (I) will be increased by doing so. As
moment of inertia I increases, its angular velocity
w
has to be decreased on the absence of external torque to
remain the
angular momentum L conserved
i.e. L = I
w
= constant (where I is moment of inertia &
w
be the angular velocity). Hence, a cat is able to land on
its feet after a fall.
91. There is
a stick made up of half wood and half steel. It is pivoted at
the wooden end and force is applied at the steel end at rt.
angle to its length. Next, it is pivoted at the steel end and
same force is applied at the wooden end. In which case, the
angular acceleration is more and why?
There is
a stick made up of half wood and half steel. It is pivoted
at the wooden end and force is applied at the steel end at
rt. angle to its length. Next, it is pivoted at the steel
end and same force is applied at the wooden end. As torque
is defined as the product of force F and perpendicular
distance R from the axis of rotation i.e.
where, I
is moment of inertia &
a
is
the angular acceleration which is defined as:
As R and F both are fixed so, the torque remains constant.
Hence, angular acceleration
a
will be more when moment of inertia I is small i.e. lighter
material at large distance from the axis of rotation i.e.
when the stick is pivoted at the steel end.
92. You are
given two eggs. One is hard boiled egg and the other raw egg.
How do you distinguish by spinning each on a tabletop?
If two
eggs are given out of which one is hard boiled egg and the
other is raw egg. When both of them are allowed to spin on a
tabletop, the egg which spins slower must be the raw egg
because the liquid inside it tries to get away from the axis
of rotation increasing the value of moment of inertia (I).
To remain the angular momentum L conserved in absence of
external torque i.e. L = I
w
= constant (where I is moment of inertia &
w
be the angular velocity), the raw egg will have less angular
velocity than the harder one. In this way, I can distinguish
two eggs by spinning each on a tabletop.
93. A fan
with blades takes longer time to come to rest than without
the blades. Why? [HSEB 1994].
As every
system will try to keep the angular momentum L conserved in
absence of external torque i.e. L = I
w
= constant (where I is moment of inertia &
w
be the angular velocity). The moment of inertia (I) of the
fan with longer blades will be greater. Hence, due to its
greater inertia of motion in rotational dynamics, its
angular velocity must decrease to conserve the angular
momentum L. Hence, a fan with blades takes longer time to
come to rest then without the blades.
94. If
the earth is struck by meteorites, it will slow down
slightly. Why? [HSEB 1996]
When
meteorites suddenly strike the earth, its mass will be
increased which increases the value of moment of inertia (I)
as the mass is directly proportional to moment of inertia.
Every system will try to keep the angular momentum L
conserved in absence of external torque i.e. L = I
w
= constant (where I is moment of inertia &
w
be the angular velocity). But its angular velocity (w)
will decrease in order to keep its angular momentum
conserved so, the earth will slow down slightly.
95. A
rifle barrel has a spiral groove, which imparts spin to the
bullet. Why?
Every
system will try to keep the angular momentum L conserved in
absence of external torque i.e. L = I
w
= constant (where I is moment of inertia &
w
be the angular velocity). The bullet acquires angular
momentum about an axis parallel to the barrel. As the
angular momentum is conserved, this keeps the bullet
pointing stably in this direction and so improves accuracy.
Hence, a spiral groove of a rifle barrel imparts spin to the
bullet.
96. How
is a swimmer jumping from a height in a swimming pool able
to increase the no of loops made in the air?
Every
system will try to keep the angular momentum L conserved in
absence of external torque. The swimmer can increase the
number of loops by pulling his legs and arms inward i.e. by
decreasing the value of moment of inertia I . As L = Iw
= constant, (where I is moment of inertia &
w
be the
angular velocity) angular velocity will be increased when
moment of inertia I is decreased. A swimmer jumping from a
height in a swimming pool is able to increase the number of
loops made in the air by pulling his legs and arms inward.
97. A
young man standing on a turntable raises his hands suddenly.
How is the turntable affected?
Every
system will try to keep the angular momentum L conserved in
absence of external torque. When hands are raised, the value
of moment of inertia I will be increased and hence, angular
velocity ,must be decreased as L = I
w
= constant (where I is moment of inertia &
w
be the angular velocity). If a young man standing on a
turntable raises his hands suddenly then the turning table
will slow down.
98.
Spokes are fitted in a cycle wheel. Why?
Every system will try to keep the angular momentum (L = I
w
=
constant) conserved (where I is moment of inertia &
w
be the
angular velocity). The spokes increase the moment of inertia
I and hence angular velocity
w
must be less to ensure angular momentum L constant. It helps
to make uniform angular speed. hence, spokes are fitted in a
cycle wheel for uniform angular speed.
99. The
handle in the flourgrinding machine is put near the
circumference, why?
A torque
is required to revolve the machine. The torque applied must
be equal to the product of force F and its perpendicular
distance r from the axis of rotation i.e.
t=
r.F
More is the distance r from the axis of rotation; the same
force F can apply more torque as
t_{
}
= r.F. Hence, the handle in the flourgrinding machine is
put near the circumference.
