Basic Mechanics (Statics) - Complete Guide

Break force vectors into their x and y components using sine and cosine to simplify solving for multiple forces. Sum the components to find the net force and direction.

Equilibrium means net forces sum to zero, with x-axis and y-axis components canceling; gravity acts downward while the normal force from the surface opposes it, keeping buildings and you static.

Resolve the 200 N rope at 30 degrees and the 196.2 N weight to find the net force at point B; the resultant has magnitude 198.12 N directed southwest.

Analyze forces on an incline in static equilibrium, identify gravity, normal force, and the push, rotate axes to the incline, and compute the required push to balance the components.

Problem 1.3 balances four forces to equilibrium by finding the missing force’s components. Fx = -3.33 N, Fy = 24.91 N, with a 25.13 N resultant at 7.6 degrees.

Calculate alpha for 75 N at 50 degrees and 120 N at unknown angle so their y components cancel (alpha ≈ 28.62°); resultant is 143.547 N in the positive direction.

Define moment as the rotation produced by a force, equal to the perpendicular distance from the rotation point times the force, computed via force components or direct distance.

Achieve equilibrium on a beam by summing forces in x and y to zero and balancing moments about a point, solving for F1 and F2.

Compute the net moment about point B from F1 and F2 using distance or components. Find the smallest force at A and the vertical middle force that matches the moment.

Compute the moment about point eight from a 220 N force at B at 40 degrees; decompose into components and use perpendicular distance to obtain net 16.7 newton meter counterclockwise.

Balance a seesaw by equating moments about point B, converting 20 kg to weight with gravity 9.81 m/s^2, and solving for mass at C using 2 m and 1.3 m.

Identify forces in a system, determine their magnitudes, and solve for the resultant or equilibrium; cover gravity, normal force, cables, buoyant force, and friction, with center of gravity.

Identify the centroid, or center of area, and relate it to the center of gravity, with triangle, rectangle, circle, and semicircle examples along symmetry axes.

Calculate the center of area for composite objects using area moments, with Xc = Qy/Area and Yc = Qx/Area, by summing each part's area times its centroid.

Explore how the center of mass aligns with the centroid and center of gravity when density is uniform, since mass equals area times thickness times density.

Explore distributed forces, including gravity as a nonuniform load, locate the resultant via the centroid, and compute magnitude from area under the load; note buoyancy increases with depth.

Understand the force of friction, including static and kinetic types, and how friction equals mu times the normal force. Coefficients depend on material to determine static or kinetic friction.

Identify the pin and roller reactions for a beam under a 40 kN/m distributed load and a 25 N point load, using equilibrium to find Ay and By.

Analyze distributed forces and buoyancy on a five by three meter object in a 1000 kg/m³ fluid. Determine the equilibrium weight using depth, area, and gravity to find the mass.

Determine weight, normal force, and friction for a car at rest on a 30-degree slope; rotate axes to align with the road and derive mu ≈ 0.58.

Identify internal forces and moments by cutting sections of a beam, apply equilibrium in x, y, and moment, and analyze internal shear and moments under a fixed support.

Explore how shear force and bending moment diagrams track internal forces along a beam, using section cuts, sign conventions, and reactions to analyze positive and negative values.

Analyze distributed loads on beams using an external resultant; generalize V(X) and M(X) for a section length X in 12 m beam example with w=1.25 N/m and 7.5 N reactions.

Learn the properties of shear and bending moment diagrams, including effects of concentrated and distributed loads, moment maxima at zero shear, and the slope relationships between load, shear, and moment.

Learn shortcuts to draw shear and bending moment diagrams from reactions and external loads, using area under the shear and type-specific segments for concentrated, distributed, and nonuniform loads.

solve problem 4.1 by computing reactions for a beam with pin and roller, resolving the distributed load into a resultant, and drawing the shear and bending moment diagrams.

Analyze a fixed beam under a trapezoidal load, a pure moment, and a endpoint force. Compute reactions and bending moments, then cut sections to derive the moment diagram.

Explore truss structures and their forces, including normal force, shear force, and bending moment, and analyze joints step by step from external reactions to internal member forces.

Explore solving trusses through external reactions, moment calculations, and joint-by-joint equilibrium, using force components, tension and compression, to ensure overall structural balance.

Explore an alternative method for solving trusses by cutting a section and treating left part as a standalone object; apply equilibrium and moments about C to find member forces efficiently.

Analyze a seven-member truss under a single external load; compute external reactions, solve joint equilibria, and determine member forces (compression or tension) using x and y components.

Solve a pin-connected truss under two external loads by first finding support reactions via moments, then analyze joints to determine all nine member forces and their tension or compression.

this lecture demonstrates solving for forces in eaf and ab using the cross-section method, applying moment equilibrium about B and A, and verifying results with problem 5.2.

Explore the moment of inertia as the rotational counterpart to mass, linking torque to angular acceleration and showing how inertia resists rotational movement around an axis.

Explore the equation of moment of inertia, I = m r^2, for any axis and point, and relate it to the second moment of area using the same form.

Explore common moment of inertia formulas for rectangle, circle, semicircle, and triangle about centroid axes, with ready equations derived from integration.

Explore the polar moment of inertia, its relation to torsion and angular acceleration, and use the radius of gyration to relate area distribution to a single point.

Use the parallel axis theorem to compute moments of inertia about any axis from the centroid value by adding area times distance squared.

Compute the moment of inertia of composite objects by summing the inertias of rectangles and triangles about a common axis, using the parallel axis theorem and centroid distances.

Substitute the rectangle’s dimensions into standard moment of inertia formulas to compute the four axes, the polar moment about the centroid, and the radius of gravitation.

Derive the moment of inertia of a circle about a tangent x-axis using the centroidal value and the parallel axis theorem, yielding I = 5/4 π r^4.

Determine the moment of inertia of a rectangle with a void about the x axis using the composite object method and the parallel axis theorem.

Calculate the centroid of distributed loads on a beam to determine the resultant force and its location from point A using moments and segment areas.