Engineering reference for Indian students

Mechanics & design

Engineering Mechanics

5 self-contained study topics — notes, diagrams, formulas, and worked examples for exams and GATE.

Topics

Force Systems and Resultants
A coplanar force system reduces to a resultant R = √(ΣF_x² + ΣF_y²) acting at θ = arctan(ΣF_y/ΣF_x), plus a moment M_O = ΣF·d. Varignon's theorem lets the moment of the resultant equal the sum of component moments, as in RK Bansal.
Free Body Diagram
A free body diagram isolates one body and shows every external force and reaction, after which equilibrium demands ΣF_x = 0, ΣF_y = 0, ΣM = 0. Correct support reactions and Newton's third-law pairs are the essence, as RK Bansal stresses.
Friction
Dry friction obeys F ≤ μ_s·N up to the point of impending motion, after which F = μ_k·N. The friction angle satisfies tanφ = μ, and belt/rope drives follow the capstan relation T₁/T₂ = e^(μθ), as in RK Bansal.
$Belt: tight side T_{1}, slack T_{2}: \frac{T_{1}}{T_{2}} = e^(\mu\theta)$
Centroid and Moment of Inertia
The centroid locates the area's geometric centre, x̄ = Σ(A·x̄ᵢ)/ΣA; the second moment of area I = ∫y²dA measures resistance to bending. The parallel-axis theorem I = Ī + A·d² shifts it to any axis, as in RK Bansal.
$Product of inertia I_{xy} = \int xy dA$
Impulse and Momentum
Linear impulse equals change of momentum: J = ∫F dt = Δ(mv). In collisions momentum is conserved and the coefficient of restitution e = (v₂ − v₁)/(u₁ − u₂) relates approach and separation speeds, as in RK Bansal.
$Conservation of momentum: Σp_{before} = Σp_{after}$