Rigid Body Dynamics

  • 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…

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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…

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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.

    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…

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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.

    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…

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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.

    (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…

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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.

    (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…

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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.

    (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…

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  • 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…

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