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Unit - I Basics and Statics of Particles Introduction - Units and dimensions - Laws of machanics - Lame's theorem, Parallelogram and triangular law of forces - Vectors - Vectorial representation of forces and moments - Vector operations : Additions, Subtraction, Dot product, Cross product - Coplanar forces - Resolution and composition of forces - Equilibrium of a particle - Forces in space - Equilibrium of a particle in space - Equivalent systems of forces - Principle of transmissibility - Single equivalant force. Unit - II Equilibrium of Rigid Bodies Free body diagram - Types of supports and their reactions - Requirements of stable equilibrium - Moments and couples - Moment of force about a point and about an axis - Vectorial representation of moments and couples - Scalar components of a moment - Varignon's theorem - Equilibrium of rigid bodies in two dimensions - Equilibrium of rigid bodies in three dimensions - Examples. Unit - III Properties of Surfaces and Solids Determination of areas and volumes - First moment of area and the centroid of sections - Rectangle, Circle, Triangle from integration - T section, I section - Angle section, Hollow section by using standard formula - Second and product moments of plane area - Rectangle, Triangle, Circle from integration - T section, I section, Angle section, Hollow section by using standard formula - Parallel axis theorem and perpendicular axis theorem - Polar moment of inertia - Principal moments of inertia of plane areas - Principal axes of inertia - Mass moment of inertia - Derivation of mass moment of inertia for rectangular section, Prism, Sphere from first principle - Relation to area moments of inertia. Unit - IV Dynamics of Particles Displacements, Velocity and acceleration, Their relationship - Relative motion - Curvilinear motion - Newton's law - Work energy equation of particles - Impulse and momentum - Impact of elastic bodies. Unit - V Friction and Elements of Rigid Body Dynamics Frictional force - Laws of Coloumb friction - Simple contact friction - Rolling resistance - Belt friction. Translation and rotation of rigid bodies - Velocity and acceleration - General plane motion.
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