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.
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
A diver in a swimming pool bends his head before diving. It ______
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?
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 ______
Three points masses, each of mass m are placed at the corners of an equilateral triangle of side l. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining other two vertices, will be ______.
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.
A flywheel of mass 20 kg and radius 5 cm is revolving at a speed of 300 rpm. Its kinetic energy is ______.
If I1 is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre of mass and I2 is the moment of inertia of the ring formed by bending the rod about an axis perpendicular to the plane, the ratio of I1 and I2 is ____________.
Moment of inertia of earth about its axis of rotation is ____________.
From a disc of mass 'M' and radius 'R', a circular hole of diameter 'R' is cut whose rim passes through the center. The moment of inertia of the remaining part of the ruse about perpendicular axis passing through the center is ______.
The moment of inertia of a body initially at rest about a given axis is 1.2 kg m2. On applying an acceleration of 25 rad/s2, the time it will take to acquire a rotational kinetic energy of 1500 J is ____________.
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 ______.
The moment of inertia of a ring about an axis passing through its centre and perpendicular to its plane is 'I'. It is rotating with angular velocity 'ω'. Another identical ring is gently placed on it so that their centres coincide. If both the ring are rotating about the same axis, then loss in kinetic energy 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 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 ______.
