Find forces required to hold a particle in equilibrium when subjected to a downward load.  Directions of the reactions are given.  

No description given

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Find the force required to produce a given moment, or vice-versa.

Determine the single force which is equivalent to a force and a couple.

Replace three tangential forces with an equivalent force-couple system acting at the center of a circle.

Solve for an angle which will result in equilibrium for a triangle subjected to three couples.   A trial and error solution is recommended.

Find the sum of two couples in a plane.

Calculate the moment of a force about three points using the definition of a Moment.  All forces and points are in the same plane.

Find the tension in a rope necessary to prevent a bracket from rotating by applying $\Sigma M = 0$.

Determine the moment of a force about a point by using $M= F d_\perp$ or $M = F_\perp d$.

Calculate the moment of a force about three points using Verignon' theorem.  All forces and points are in the same plane.

Find the moment of a couple formed by two equal and opposite forces.

Replace two parallel forces with an equivalent single force

Equilibrium of two interacting particles.

Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Determine the resultant of three random 2-D vectors.  

Find the magnitude and direction of a force give its scalar components.

Find the rectangular (scalar) components of a force for two coordinates systems.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

Find the reactions of a rigid body (a triangular plate) at a pin and roller.  The load is at an angle.

Classic problem of a vehicle parked on an incline.  Best solved by rotating the coordinate system.

Image Credit: https://svgsilh.com/image/34325.html  CC-0

A hand truck on wheels.  Easiest to solve by rotating coordinate system.

Find the reactions of a rigid body (a triangular plate) at a pin and roller, using the three-force body principle.

Equilibrium of a rigid body.  Find tension to raise a pole.

Find the reactions of a rigid body (a truss) at a pin and roller.  All loads are either horizontal or vertical.

Rigid body equilibrium problem.  Easiest to solve by replacing forces on the perimiter of the pulley with equivalent forces at the axle.