Solve for the internal force in three members of a truss.

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

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

Two forces act on a bell crank. This problem has two unknown magnitudes and an unknown direction which makes it tricky to solve by the equilibrium equation method.  

The solution is much simpler if three force body principle is used.

Two known forces, and a third with known magnitude act on a rigid body.  Apply $\Sigma M = 0$ about a pin restraint to determine the direction of the third force.  The problem has two valid answers.

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

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

Two dimensional particle equilibrium problem.  Advice shows how to use how to use slope triangles to find sines and cosines, rather than finding the angle and using that.

Replace two forces with a equivalent force-couple system at a specified point.

3D equilibrium of a particle problem.  Rectangular steel plate supported by three cables, dimensions and density given.

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

Determine frictional force acting on a block on an incline.  Coefficients of friction, weight and a horizontal force are given

Replace two parallel forces with an equivalent single force

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

Find the tensions is a system of cables supporting two loads.

Simple truss with a zero-force member

An A-frame structure supporting a load at the top.  Simple because both legs are two force bodies.

This just an equilibrium of a particle problem, but posed in context of a joint as a warm-up for the method of joints.

Advice is brief.

Derive the expressions for the shear and bending moment as functions of $x$ for a cantilever beam with a uniformly varying (triangular) load.

Find the forces in the members of a truss using the method of joints.

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

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

Gives a plot of a velocity-time graph using JSXgraph, and a description of the motion shown in the graph. The student is asked to calculate the acceleration at different stages of the motion, and the displacement at the end of the motion.

Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.  

Given the moment of inertia of an area about an arbitrary axis, find the centroidal moment of inertia and the moment of inertia about a second axis.

Write expressions for the moment of inertia of simple shapes about various axes.