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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 =ml2a. 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 I1 and I2 (I1>I2) and equal angular momentum. Which one has greater K.E.?

The moment of inertia of two rotating bodies are I1 and I2 (I1>I2) and equal angular momentum i.e. L1 = L2 = 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 I1>I2  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 vice-versa 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 flour-grinding 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 flour-grinding machine is put near the circumference.

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