Define Moment Of Inertia And Product Of Inertia For A Rigid Body.
Moment of inertia & Product of inertia: The angular momentum of of a rigid body in vector notation can be represented as where, is the moment of inertia tensor. The…
Obtain An Expression For The Moment Of Inertia Of A Solid Cone (i) About Its Axis Of Symmetry, (ii) About An Axis Passing Through The Vertex And Perpendicular To The Axis Of Symmetry
(i) Moment of inertia of a solid cone about its axis of symmetry: Fig. 1 Let us consider a right circular solid cone ABC of mass M and height h,…
Determine The Moment Of Inertia Of A Triangular Lamina (i) About One Of Its Sides, (ii) About An Axis Passing Through The Centre Of Gravity And Parallel To One Side, (iii) About An Axis Passing Through One Of Its Vertices And Parallel To Opposite Side.
(i) Moment of inertia of a triangular lamina about one of its side: Fig. 1 Let us consider a triangular lamina ABC of mass M, is rotating about one of…
Determine The Moment Of Inertia Of A Uniform Elliptic Lamina Or Elliptic Disc (i) About Its Minor Axis, (ii) About Its Major Axis, (iii) About An Axis Passing Through The Centre Of The Disc And Perpendicular To Its Plane.
(i) Moment of inertia of a uniform elliptic lamina or elliptic disc about its minor axis: Fig. 1 Let us consider a uniform elliptic lamina or elliptic disc of mass…
Calculate The Moment Of Inertia Of A Circular Ring (i) About An Axis Passing Through Its Centre And Perpendicular To The Plane Of The Ring, (ii) About An Axis Passing Through Its Centre And Lying In The Plane.
(i) Moment of inertia of a circular ring about an axis passing through its centre and perpendicular to the plane of the ring: Fig. 1 Let us consider a circular…
Determine The Moment Of Inertia Of Rectangular Lamina (i) About An Axis Parallel To Its Breadth And Passing Through Its Centre Of Mass, The Axis Lying In The Plane Of The Lamina, (ii) About An Axis Parallel To Its Length And Passing Through Its Centre Of Mass, The Axis Lying In The Plane Of The Lamina, (iii) About An Axis Passing Through Its Centre Of Mass And Perpendicular To The Plane Of The Lamina.
(i) Moment of inertia of rectangular lamina about an axis parallel to its breadth and passing through its centre of mass: Fig. 1 Let us consider a rectangular lamina ABCD…
Calculate The Moment Of Inertia Of A Thin Uniform Rod (i) About An Axis Passing Through Its Centre And Perpendicular To Its Length, (ii) About An Axis Passing Through One Of Its End And Perpendicular To Its Length.
(i) Moment of inertia of a thin uniform rod about an axis passing through its centre and perpendicular to its length: Fig. 1 Let us consider a thin uniform rod…
Calculate The Moment Of Inertia Of A Thin Spherical Shell (i) About A Diameter, (ii) About Its Tangent.
Moment of inertia of a thin spherical shell about a diameter: Let us consider, a spherical shell of radius r and mass M. The surface area of this spherical shell…
Calculate The Moment Of Inertia Of A Hollow Sphere (i) About A Diameter, (ii) About A Tangent, (iii) About An Axis Through The Centre Of The Hollow Sphere.
(i) Moment of inertia of a hollow sphere about a diameter: Fig. 1 Let us consider a hollow sphere of inner radius and outer radius . So the volume of…
Derive An Expression For Moment Of Inertia Of A Uniform Solid Sphere (i) About A Diameter, (ii) About A Tangent, (iii) About An Axis Passing Through The Centre.
(i) Moment of inertia of a uniform solid sphere about one of its diameter: Fig. 1 Let us consider a uniform solid sphere of radius r and mass M, rotating…