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 ______.
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 ______
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
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 ______.
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 flywheel of mass 20 kg and radius 5 cm is revolving at a speed of 300 rpm. Its kinetic energy 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 ____________.
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 ______.
Figure shows triangular lamina which can rotate about different axis of rotation. Moment of inertia is maximum about the axis ______.

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?
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 ______.
The moment of inertia of a body about a given axis is 1.2 kg-m2. Initially, the body is at rest. In order to produce, a rotational kinetic energy of 1500 J, an acceleration of 25 rad/s2 must be applied about that axis for a duration of ______.
Two discs A and B of same material and thickness have radii R and 3R respectively. Their moments of inertia about their axis will be in the ratio ______.
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 ______.
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:

