Kinetics of Rigid Bodies

7/25/2019 Kinetics of Rigid Bodies

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Planar Kinetics of Rigid Bodies


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Mass Moment of Inertia


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Mass Moment of Inertia


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Selection of dAmay be of three different types

Moment of Inertia by Integration


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Determination of Moment

of Inertia (M.I.) of rectangular

area

Determination of Moment

of Inertia (M.I.) of anArea using rectangular strip

Setting b=dxand h=y, we can write

Examples


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For solution of part (a) find M.I. by taking

Three types of element as described in Slide 5

(a) Determine the moment of inertia of the shaded area shown in figure to

each co-ordinate axes; (b) Using the results of part a, determine the radius

of gyration of the shaded area with respect to each of the co-ordinate axes.

Answer:

Examples


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Parallel axis theorem


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Parallel axis theorem


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Radius of Gyration


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Moment of Inertia of Common Shapes


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It is defined as

Unlike Ixand Iy, Ixycan be +ve, -ve, or zero

When one or both the axes are symmetry, Ixy=0, for example

Parallel axis theorem in terms of centroid C position as shown below

can be written as

Product Moment of Inertia


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Planar Kinetics Equation of Motion

Equation of Translat ional Motion


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Equation of Translational Motion

Rectilinear Translation


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Equation of Translational Motion

Curvilinear Translation


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Equation of Rotational Motion


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Rotation about a fixed axis


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Free body DiagramKinetic Diagram


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Work and Energy


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Kinetic Energy


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Work done by a Force

Variable force Constant force


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Weight Spring Force

Work done by a Force


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Work done by a Couple Moment


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Potential Energy


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Principle of Conservation of Energy


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Impu lse and Momentum


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Linear and Angular Momentum


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Principle of Impulse and Momentum


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Kinetics of Rigid Bodies