Advertisements
Advertisements
प्रश्न
Discuss conservation of angular momentum with example.
Advertisements
उत्तर
When no external torque acts on the body, the net angular momentum of a rotating rigid body remains constant. This is known as the law of conservation of angular momentum.
τ = `"dL"/"dt"`
If τ = 0 then, L = constant.
As the angular momentum is L = Iω, the conservation of angular momentum could further be written for initial and final situations as,
Iiωi = Iiωi (or) Iω = constant
The above equations say that if I increase ω will decrease and vice – versa to keep the angular momentum constant.
conservation of angular momentum for ice dancer
There are several situations where the principle of conservation of angular momentum is applicable. One striking example is an ice dancer as shown in Figure A. The dancer spins slowly when the hands are stretched out and spins faster when the hands are brought close to the body.
Stretching of hands away from body increases moment of inertia, thus the angular velocity decreases resulting in a slower spin. When the hands are brought close to the body, the moment of inertia decreases, and thus the angular velocity increases resulting in a faster spin. A diver while in the air as in Figure B curls the body close to decrease the moment of inertia, which in turn helps to increase the number of somersaults in the air.
conservation of angular momentum for a diver
APPEARS IN
संबंधित प्रश्न
A thin walled hollow cylinder is rolling down an incline, without slipping. At any instant, without slipping. At any instant, the ratio "Rotational K.E.: Translational K.E.: Total K.E." is ______.
On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?
While driving along an unbanked circular road, a two-wheeler rider has to lean with the vertical. Why is it so? With what angle the rider has to lean? Derive the relevant expression. Why such a leaning is not necessary for a four wheeler?
The coefficient of static friction between a coin and a gramophone disc is 0.5. Radius of the disc is 8 cm. Initially the center of the coin is 2 cm away from the center of the disc. At what minimum frequency will it start slipping from there? By what factor will the answer change if the coin is almost at the rim? (use g = π2m/s2)
Answer in Brief:
A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10 kg and a radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the center. Calculate x if the wheel now rotates at 80 rpm.
A body weighing 0.5 kg tied to a string is projected with a velocity of 10 m/s. The body starts whirling in a vertical circle. If the radius of the circle is 0.8 m, find the tension in the string when the body is at the top of the circle.
A particle undergoes uniform circular motion. The angular momentum of the particle remains conserved about, ______
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along, ______
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature to a certain value, its speed of rotation ______.
A ring and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque τ on the ring, it stops after completing n revolution in all. If the same torque is applied to the disc, how many revolutions would it complete in all before stopping?
