Advertisements
Advertisements
Question
State the law of conservation of angular momentum and explain with a suitable example.
Advertisements
Solution
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.
APPEARS IN
RELATED QUESTIONS
Obtain an expression for the torque acting on a rotating body with constant angular acceleration. Hence state the dimensions and SI unit of torque.
A stone is tied to one end of a string. Holding the other end, the string is whirled in a horizontal plane with progressively increasing speed. It breaks at some speed because ______
A 500 kg car takes a round turn of the radius of 50m with a velocity of 36 km/hr. The centripetal force is ______.
A flywheel is revolving with a constant angular velocity. A chip of its rim breaks and flies away. What will be the effect on its angular velocity?
An electron(e) is revolving in a circular orbit of radius r in the hydrogen atom. The angular momentum of the electron is (M = magnetic dipole moment associated with it and m = mass of electron)
Angular momentum of the earth revolving around the sun is proportional to rn , where r is the distance between the earth and the sun. Value of n is ____________.
If the angular momentum of a body increases by 50%, then its kinetic energy of rotation increases by ______ (M.I. remains constant)
If the kinetic energy of rotation of a body is doubled, then its angular momentum ____________.
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 ____________.
Let I1 and I2 be the moments of inertia of two bodies of identical geometrical shape. If the first body is made of aluminium and the second of iron, then ____________.
mass is whirled in a circular path with constant angular velocity and its linear velocity is v. If the string is now halved keeping the angular momentum same, the linear velocity is ______.
Earth revolves round the sun in a circular orbit of radius 'R'. The angular momentum of the revolving earth is directly proprtional to ______.
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 ____________.
lf 'I' is the moment of inertia and 'L' is angular momentum of a rotating body, then `L^2/(2I)` is its ______.
Three-point masses each of mass 'M' are placed at the corners of an equilateral triangle of side 'a'. The moment of inertia of this system about an axis passing through one side of a triangle is ______.
An electron in an atom is revolving round the nucleus in a circular orbit of radius 5.3 × 10-11 m with a speed of 3 × 106 m/s. Find the angular momentum of electron.
A body is rotating about its own axis. Its rotational kinetic energy is x and its angular momentum is y, hence its moment of inertia about the axis 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 ______.
Define moment of inertia.
Define angular momentum.
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)
