Force vectors, equilibrium, free-body diagrams, trusses, frames, friction, centroids and moments of inertia.
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- What is the method for adding two force vectors using rectangular components?
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Resolve each force into x and y components, add the components separately, then find the resultant using the Pythagorean theorem.- Define a resultant force.
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A single force that has the same effect as two or more forces acting together.- What is a unit vector in force notation?
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A vector with magnitude 1 used to indicate direction; a force is expressed as magnitude times a unit vector.- How do you find the component of a force in a given direction using the dot product?
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F_component = F dot u, where u is the unit vector in the desired direction.- The cross product of two forces gives what quantity?
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The moment (or torque) about a point.- What does the magnitude of a cross product represent physically?
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The area of the parallelogram formed by the two vectors, or the moment magnitude.- State the two conditions for static equilibrium of a rigid body in 2D.
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Sum of all forces in x and y directions equals zero, and sum of all moments about any point equals zero.- How many scalar equations can be written for equilibrium of a 3D rigid body?
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Six equations: three for force equilibrium (x, y, z) and three for moment equilibrium (about x, y, z axes).- What is the difference between equilibrium of particles and equilibrium of rigid bodies?
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Particles only require sum of forces to be zero; rigid bodies require both sum of forces and sum of moments to be zero.- Define a concurrent force system.
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A system where all forces act through a single point, so no moment is produced.- In a parallel force system, what condition must be satisfied for equilibrium?
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The sum of all forces must be zero and the sum of moments about any point perpendicular to the forces must be zero.- What is a general force system?
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A system with forces acting in different directions and at different points, requiring all six equilibrium equations in 3D.- What is the primary purpose of a free-body diagram?
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To isolate and show all forces and moments acting on an object, making it easier to apply equilibrium equations.- How many reaction forces does a pin support produce?
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Two reaction forces: one horizontal (Ax) and one vertical (Ay).- How many reaction forces does a roller support produce?
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One reaction force perpendicular to the surface it rolls on.
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