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What Is A Rigid Body?
Rigid body: A rigid body is a system of particles (an assembly of a large number of particles), in which the distance of the inter-particle remains unchanged when it is acted upon by an external force or torque. The rigid body is a system of mass points and the distances between all pairs of points…
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Derive An Expression For The Kinetic Energy Of A Rotating Body.
Kinetic energy of rotating body: Let us consider a rigid body of mass M is rotating about a fixed axis with an uniform angular velocity . Let us consider, the rigid body consists of a large number of particles of masses , , etc, situated at distances , , etc, respectively from the axis of…
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Define The “Moment of Inertia”.
Moment of inertia: Let us consider, a rigid body is rotating about an fixed axis with a uniform angular velocity . This rigid body consists of a large number of particles of masses , , etc. and the distance of these particles from the axis of rotation are , , etc. respectively. Then the rotational…
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Define ‘Radius Of Gyration’.
Radius of gyration: Let us consider that a rigid body consists of n number of particles, each of the same mass m. So the total mass of the rigid body is . Let , , , be the distances of the particles from the axis of rotation. So the moment of inertia of the body…
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What Is The Physical Significance Of Moment Of Inertia?
Physical significance of moment of inertia: According to Newton’s 1st law of motion, the stationary object is fixed forever and the moving object continues to move along a straight line with constant speed, unless the object is forced to change its state of rest or of uniform motion by an external force. Greater the mass…
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Derive A Relation Between Angular Momentum And Moment Of Inertia.
Relation between angular momentum and moment inertia: Let us consider that a rigid body consists of a large number of particles of masses , , , etc., rotating about a fixed axis with a uniform angular velocity . Let , , , etc. be the distances of the masses , , , etc respectively from…
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Derive A Relation Between Torque And Moment Of Inertia.
Relation between torque and moment of inertia: Let us consider that a rigid body consists of a large number of particles of masses , , , etc., rotating about a fixed axis with a uniform angular acceleration . Let , , , etc. be the distances of the masses , , , etc respectively from…
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State And Prove The Theorem Of Parallel Axes.
Parallel Axes Theorem: Parallel axis theorem states that the moment of inertia of a body about any axis is equal to the sum of its moment of inertia about a parallel axis passing through the centre of mass of the body and the product of the mass of that body and the square of the…
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State And Prove The Theorem Of Perpendicular Axes.
Perpendicular axes theorem (laminar body): The perpendicular axes theorem states that the sum of moments of inertia of a plane laminar body about any two mutually perpendicular axes in the plane of that laminar body is equal to the moment of inertia of the plane laminar body about a third axis which passes through the…
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Determine The Moment Of Inertia Of A Plane Circular Disc (i) About An Axis Through Its Centre And Perpendicular To Its Plane, (ii) About A Diameter, (iii) About A Tangent, (iv) About An Axis Tangential To The Disc And Perpendicular To Its Plane.
(i) Moment of inertia of a plane circular disc about an axis through its centre and perpendicular to its plane: Let us consider a circular disc of radius r and mass M, rotating about a fixed axis MN, which passes through its centre O at a right angle to the plane of the disc. Now…
