Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given, m = 10 kg
r = 60 cm
r = 60 × 10-2 m
l = ?
Moment of inertia of a uniform disc
l = `"mr"^2/2`
`= (10 xx (60 xx 10^-2)^2)/2`
`= (10 xx 3600 xx 10^-4)/2`
= 1.8 kgm2
Moment of inertia of a uniform disc is 1.8 kg m2.
APPEARS IN
RELATED QUESTIONS
A diver in a swimming pool bends his head before diving. It ______.
Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, then what is the ratio of their angular velocity.
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.
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)
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 ______.
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 ____________.
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 ______.
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 ______.
Moment of inertia of the rod about an axis passing through the centre and perpendicular to its length is 'I1'. The same rod is bent into a ring and its moment of inertia about the diameter is 'I2', then `"I"_2/"I"_1` 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 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`)
The moment of inertia of a circular disc of mass M and radius R about an axis passing through the centre of mass is I0. The moment of inertia of another circular disc of same mass and thickness but half the density about the same axis is ______.
For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular cross-section 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 ______.

Four point masses, each of mass ‘m’ are arranged in X-Y plane as shown in the figure. The moment of inertia of this system about X-axis is:

