Advertisements
Advertisements
Question
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?
Advertisements
Solution
Given:
I = 1.2 kgm2, α = 25 radian/sec2, ω0 = 0 rad/s, (K.E.)rot = 1500 J
To find: Time (t)
Formulae:
i. α = `(ω - ω_0)/t`
ii. K.E. = `1/2"Iω"^2`
Calculation:
From formula (i),
25 = `(ω - 0)/t`
∴ ω = 25t
From formula (ii),
1500 = `1/2 xx 1.2 xx (25t)^2`
∴ t = `sqrt((2 xx 1500)/(1.2 xx 25^2)) = sqrt4`
∴ t = 2 sec.
An angular acceleration must be applied for 2 sec.
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.
A thin uniform rod has mass M and length L The moment of inertia about an axis perpendicular to it and passing through the point at a distance `"L"/3` from one of its ends, will be ______.
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 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 ____________.
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.
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 ______.
A cord is wound round the circumference of a wheel of radius 'r'. The axis of the wheel is horizontal and moment of inertia about it is T. A block of mass 'm' is attached to free end of the cord, initially at rest. When the wheel rotates and the block moves vertically downwards through distance 'h', the angular velocity of the wheel will be ______.
(Neglect the mass of cord, g =acceleration due to gravity)
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 ____________.
The moment of inertia of a sphere is 20 kg-m2 about the diameter. The moment of inertia about any tangent 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 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`)
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.
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 ______.
The moment of inertia (MI) of a disc of radius R and mass M about its central axis is ______.
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 ______.
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 ______.
