Author: Physics Notebook
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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.
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(i) Moment of inertia of a uniform elliptic lamina or elliptic disc about its minor axis: Let us consider a uniform elliptic lamina or elliptic disc of mass M, semi-major axis a and semi-minor axis b. So the total surface area of this elliptic lamina is and the mass density i.e., mass per unit surface…
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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.
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(i) Moment of inertia of a circular ring about an axis passing through its centre and perpendicular to the plane of the ring: Let us consider a circular uniform ring of radius and mass , rotating about an axis PQ passing through its centre and perpendicular to the plane of the ring. So the length…
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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.
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(i) Moment of inertia of rectangular lamina about an axis parallel to its breadth and passing through its centre of mass: Let us consider a rectangular lamina ABCD of mass M, length and breadth . So the surface area of this rectangular lamina is and mass density i.e., mass per unit area of this lamina…
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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.
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(i) Moment of inertia of a thin uniform rod about an axis passing through its centre and perpendicular to its length: Let us consider a thin uniform rod AB of mass M and length . So the mass density i.e., mass per unit length of this rod is . In order to calculate the moment…
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Calculate The Moment Of Inertia Of A Thin Spherical Shell (i) About A Diameter, (ii) About Its Tangent.
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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 is . So the mass density i.e., mass per unit area of this spherical shell is . In order to calculate the moment of inertia…
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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.
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(i) Moment of inertia of a hollow sphere about a diameter: Let us consider a hollow sphere of inner radius and outer radius . So the volume of this hollow sphere is . If M be the mass of the hollow sphere, then mass density i.e., mass per unit volume of the hollow sphere is…
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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.
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(i) Moment of inertia of a uniform solid sphere about one of its diameter: Let us consider a uniform solid sphere of radius r and mass M, rotating about one of its own diameter PQ. So the volume of this solid sphere is and the mass density i.e., mass per unit volume is . To…
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Obtain An Expression For The Moment Of Inertia Of A Hollow Cylinder (i) About Its Own Axis, (ii) About An Axis Passing Through The Centre Of Mass Of The Cylinder And Perpendicular To Its Length.
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(i) Moment of inertia of a hollow cylinder about its own axis: Let us consider a hollow cylinder of inner radius , outer radius and length . So the volume of this hollow cylinder is . The cylinder is rotating about its own AB. Let be the mass of this hollow cylinder, so the mass…
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Calculate The Moment Of Inertia Of A Solid Circular Cylinder (i) About Its Own Axis, (ii) About An Axis Passing Through Its Centre Of Mass And Perpendicular To Its Length.
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Moment of inertia of a solid circular cylinder about its own axis: Let us consider a solid circular cylinder of length l and radius r be rotating about its own axis AB. So the volume of the cylinder is . Let M be the mass of the cylinder, so the mass density i.e., mass per…
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Determine The Moment Of Inertia Of An Annular Disc Or Ring (i) About An Axis Through Its Centre And Perpendicular To Its Plane, (ii) About A diameter, (iii) About A Tangent In Its Own Plane, (iv) About A Tangent Perpendicular To Its Plane.
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An annular disc is a flat circular ordinary disc, which has a concentric circular hole in it. (i) Moment of inertia of an annular ring or disc through its centre and perpendicular to its plane: Let us consider an annular ring or disc of inner radius and outer radius , rotating about an axis PQ…