An addendum to Kravis: an appreciative note on hating one's work

The work done by an external force on a particle changes its kinetic energy. However, internal forces must also be considered for a system of interacting particles. The potential energy formulation helps formulate the effect of internal forces. The net work done by an external force can be written in terms of the total change of mechanical energy, which includes both kinetic and potential energies.
In the presence of a non-conservative opposing force, like friction, some part of the work done...

Mechanical engineering involves the study of motion, energy, and force, and is concerned with designing, manufacturing, and maintaining mechanical systems. One important concept in this field is the couple moment, produced by two equal and opposite forces acting at two points in a rigid body separated by a certain distance.
When the rigid body undergoes a differential displacement due to a couple, its motion can be divided into two parts: equal translation of the two points to their final...

As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroundings to the system.

The total work done on an object acted upon by multiple forces can be computed using two methods that give the same result. In one method, the work done by each force is first calculated. Then, those values are summed algebraically to calculate the total work done by all the forces. In the second method, the net force is first calculated by a vector sum of all the forces. Then, the work done by this force is obtained.
Since forces perpendicular to the displacement do no work, they do not...

The center-of-mass framework helps to easily describe the work done on rigid bodies. Since the internal forces in a rigid body do no work, they can be ignored, and the external forces can be considered in the work-energy theorem.
The work done by gravity to move a rigid body, or the work done by an opposing force to move a rigid body against gravity, can be calculated using the center-of-mass framework. It is the line integral of the force of gravity over the path, considered positive if...

The principle of virtual work states that if a body is in static and dynamic equilibrium, then the sum of all the virtual work done by all external forces and couple moments for any given virtual displacement must be zero.
In static equilibrium, a body can experience an imaginary or virtual movement, such as displacement or rotation. The virtual work done by a force is equal to the dot product of force and virtual displacement in the direction of the force. When it comes to virtually rotating a...