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प्रश्न
State the law of conservation of angular momentum and explain with a suitable example.
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उत्तर
Statement: The angular momentum of a body remains constant if the resultant external torque acting on the body is zero.
Example:
- A ballet dancer makes use of the law of conservation of angular momentum to vary her angular speed.
- The torque acting on her body is zero. By the law of conservation of angular momentum, L = constant
Iω = constant ⇒ ω ∝1/I - When she suddenly folds her arms and brings the stretched leg close to the body, her angular velocity increases on account of the decrease in moment of inertia. This helps in rotating safely on her legs.
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संबंधित प्रश्न
Obtain an expression for torque acting on a body rotating with uniform angular acceleration.
A flywheel of mass 8 kg and radius 10 cm rotating with a uniform angular speed of 5 rad/sec about its axis of rotation, is subjected to an accelerating torque of 0.01 Nm for 10 seconds. Calculate the change in its angular momentum and change in its kinetic energy.
A stone of mass 1 kg is rotated in a horizontal circle of radius 0.5 m. If it makes `100/pi` rps, then its angular momentum is ______
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If the angular momentum of a body increases by 50%, then its kinetic energy of rotation increases by ______ (M.I. remains constant)
A thin metal wire of length 'L' and uniform linear mass density 'ρ' is bent into a circular coil with 'O' as centre. The moment of inertia of a coil about the axis XX' is ______.
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The ratio of the dimensions of Planck's constant to that of moment of inertia is the dimensions of ______.
If the angular momentum of an electron is `vec"J"` then the magnitude of the magnetic moment will be ____________.
A homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 radian/s. The linear momentum of the disc is ____________.
An electron has a mass of 9.1 x 10-31 kg. It revolves round the nucleus in a circular orbit of radius 0.529 x 10-10 metre at a speed of 2.2 x 106 m/s. The magnitude of its linear momentum in this motion is ____________.
The direction of angular momentum of particle is ____________.
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lf 'I' is the moment of inertia and 'L' is angular momentum of a rotating body, then `L^2/(2I)` is its ______.
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A particle of mass m = 5 unit is moving with a uniform speed v = 3`sqrt2` unit in the XY-plane along the line y = x + 4. The magnitude of the angular momentum about origin is ______.
A sphere rolls without slipping on a rough horizontal surface with centre of mass speed v0. If mass of the sphere is M and its radius is R, then what is the angular momentum of the sphere about the point of contact?
The angular momentum of the electron in the second orbit of hydrogen atom is L. The angular momentum in the third orbit is ______.
Calculate the change in angular momentum of the electron when it jumps from third orbit to first orbit in hydrogen atom.
(Take h = 6.33 × 10−34 Js)
Two whistles A and B have frequencies 660 Hz and 590 Hz respectively. An observer is standing in the middle of the line joining the two sources. he middle of the line joining the two sources. Source B and observer are moving towards right with velocity 30 m/s and A is stationary at left side. The number of beats listened by the observer are ______.
(Velocity of sound in air = 300 m/s)
