Advertisements
Advertisements
प्रश्न
Two wheels of the moment of inertia 4 kgm2 rotate side by side at the rate of 120 rev/min and 240 rev/min respectively in the opposite directions. If now both the wheels are coupled by means of a weightless shaft so that both the wheels rotate with a common angular speed. Calculate the new speed of rotation.
Advertisements
उत्तर
I1 = I2 = I = 4 kg m2 , n1 = 120 r.p.m, n2 = 240 r.p.m.
Initially, the angular velocities of the two wheels are `vecω_1` and `vecω_2` and, therefore the angular momentum `vecL_1` and `vecL_2` are in opposite directions.
∴ The magnitude of the total initial angular momentum, L = -L1 + L2
∴ L = -Iω1 + Iω2 .................(i)
After coupling on the same shaft, the total moment of inertia is 2I.
Let, ω = 2πn be the common angular speed.
∴ The magnitude of the total final angular momentum L′ = 2Iω ….(ii)
By the principle of conservation of angular momentum, L = L′
∴ Equating equation (i) and (ii), we have
I(ω2 − ω1) = 2Iω
∴ 2 × 2πn = 2π(n2 - n1)
∴ 2n = n2 − n1
∴ n = `(n_2 - n_1)/2 = (240 - 120)/2` = 60 r.p.m.
The new speed of rotation of the wheels would be 60 r.p.m.
APPEARS IN
संबंधित प्रश्न
The moment of inertia of a circular loop of radius R, at a distance of R/2 around a rotating axis parallel to horizontal diameter of the loop is ______
The moment of inertia of a body about a given axis is 1.2 kgm2. initially, the body is at rest. For what duration on the angular acceleration of 25 radian/sec2 must be applied about that axis in order to produce rotational kinetic energy of 1500 joule?
A uniform disc of radius ' a' and mass 'm' is rotating freely with angular speed 'ω' in a horizontal plane, about a smooth fixed vertical axis through its centre. A pa1ticle of mass 'm' is then suddenly attached to the rim of the disc and rotates with it. The new angular speed is ______
A particle starting from rest moves along the circumference of a circle of radius r with angular acceleration a. The magnitude of the average velocity, in the time it completes the small angular displacement θ is
Surface density of charge on a charged conducting sphere of radius R in terms of electric field intensity E at a distance r in free space is ____________.
(r > R, ε0 = permittivity of free space)
The moment of inertia of a uniform thin rod of length L and mass M about an axis passing through a point at a distance of L/3 from one of its ends and perpendicular to the rod is ______
If radius of the solid sphere is doubled by keeping its mass constant, the ratio of their moment of inertia about any of its diameter is ______.
Four solid spheres each of mass M and radius R are placed with their centres on the four comers of a rectangle. If b is a breadth of rectangle and its length is twice of its breadth, then find moment of inertia of the system about an axis along one of the breadth of the rectangle.
Three identical rods each of mass 'M' and length 'L' are joined to form a symbol 'H'. The moment of inertia of the system about one of the sides of 'H' is ______.
A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz. The acceleration of the particle in m/s2 is ______.
A flywheel of mass 20 kg and radius 5 cm is revolving at a speed of 300 rpm. Its kinetic energy is ______.
A rod of length 1 m and mass `1/2` kg rotates at an 2 angular speed of 6 rad s-1 about one of its ends. The kinetic energy of the rod is ______.
Three rings, each of mass P and radius Q, are arranged as shown in the figure. The moment of inertia of the arrangement about YY' will be ______.
Two discs having moment of inertia I1 and I2 are made from same material have same mass. Their thickness and radii are t1, t2, and R1, R2 respectively. The relation between moment of inertia of each disc about an axis passing through its centre and perpendicular to its plane and its thickness is ______.
A thin uniform rod of length 'L' and mass 'M' is bent at the middle point 'O' at an angle of 45° as shown in the figure. The moment of inertia of the system about an axis passing through 'O' and perpendicular to the plane of the bent rod, is ______.
A uniform disc of mass 4 kg has radius of 0.4 m. Its moment of inertia about an axis passing through a point on its circumference and perpendicular to its plane is ______.
A disc rolls down a smooth inclined plane without slipping. An inclined plane makes an angle of 60° with the vertical. The linear acceleration of the disc along the inclined plane is ______.
(g = acceleration due to gravity, sin 30° =cos 60° `=1/2,` sin 60° = cos 30° `=sqrt3/2`)
A thin circular ring of mas 'M' and radius 'R' is rotating about a transverse axis passing through its centre with constant angular velocity 'ω'. Two objects each of mass 'm' are attached gently to the opposite ends of a diameter of the ring. What is the new angular velocity?
Calculate the moment of inertia of a uniform disc of mass 10 kg and radius 60 cm about an axis perpendicular to its length and passing through its center.
A disc of radius R and thickness `"R"/6` has moment of inertia/about an axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is ______.
The moment of inertia (MI) of a disc of radius R and mass M about its central axis is ______.
Two spheres each of mass M and radius R are connected with a massless rod of length 4 R. The moment of inertia of the system about an axis passing through the centre of one ofthe spheres and perpendicular to the rod will be ______.
If two circular rings A and B are of same mass but of radii r and 2r respectively, then the moment of inertia about an axis passing through C.G. and perpendicular to its plane, of A is ______.
