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.
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 ______
The moment of inertia of a uniform circular disc about a tangent in its own plane is 5/4MR2 where M is the mass and R is the radius of the disc. Find its moment of inertia about an axis through its centre and perpendicular to its plane.
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?
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
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 ______.
Two rods, each of mass m and length l, are joined as shown in the figure. Moment of inertia of system about an axis passing through one end of the rod, i.e. O, and perpendicular to the plane 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 ______.
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 ______.
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 ______.
Figure shows triangular lamina which can rotate about different axis of rotation. Moment of inertia is maximum about the axis ______.
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 ______.
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 ______.
