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Moment of inertia of shell 1 along diameter
Moment of inertia of shell . i of shell 3
So, of the system along
or,
A rod of weight is supported by two parallel knife edges and and is in equilibrium in a horizontal position. The knives are at a distance from each other. The centre of mass of the rod is at distance from . The normal reaction on is
By torque balancing about
The tension in the string is increased gradually and finally moves in a circle of radius . The final value of the kinetic energy is
Applying angular momentum conservation
Therefore, new
A force is acting at a point . The value of for which angular momentum about origin is conserved is
2
zero
1
-1
Given: Radius of disc,
angular acceleration ; time
Particle at periphery (assume) will have both radial (one)
and tangential acceleration
From equation,
Net acceleration,
A uniform circular disc of radius at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of . Its net acceleration in at the end of is approximately :
8.0
7.0
6.0
3.0
Moment of inertia of complete disc about point ' '.
Mass of removed disc
(Mass area)
Moment of inertia of removed disc about point ' '.
(about same perpendicular axis)
Therefore the moment of inertia of the remaining part of the disc about a perpendicular axis passing through the centre,
From a disc of radius and mass , a circular hole of diameter , whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?
Centre of mass may or may not coincide with centre of gravity. Net torque of gravitational pull is zero about centre of mass.
Mechanical advantage, M. A.
(A) Centre of mass of a body always coincides with the centre of gravity of the body
(B) Centre of mass of a body is the point at which the total gravitational torque on the body is zero
(C) A couple on a body produce both translational and rotation motion in a body
(D) Mechanical advantage greater than one means that small effort can be used to lift a large load
(A) and (B)
(B) and (C)
(C) and (D)
(B) and (D)
If M.A. Load Effort16. (a) Here,
Loss in K.E.
Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities and . They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:
Given, mass of cylinder
?
As we know, torque
.
A rope is wound around a hollow cylinder of mass and radius . What is the angular acceleration of the cylinder if the rope is pulled with a force of ?
A solid cylinder of mass and radius is rotating about its axis at the rate of . The torque required to stop after revolutions is :
Given : Force, N
Position vector,
Torque,
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