Work-Energy theorem is a fundamental basis of handling problems involving physical situations in
several domains of physics where energy transformations take place. Whenever some work is done by a
force it is equal to the decrease in energy of the agent who is doing the work and same amount of
energy increases in the body/agent on which work is done.
If work is done on/by a rigid body, it is equal to change in kinetic energy of body if only mechanical
energy is involved as rigid body cannot store potential energy in its own. This is the basis we use for
application of Work-Energy Theorem while using it for rigid bodies.
To understand basics of Work-Energy Theorem follow the video – https://youtu.be/uvNZu1yy9Co
Relation in Potential Energy and Force: We know that Potential Energy is a characteristic of
Conservative force fields only where no dissipation of energy take place. Whenever some work is done
on or by an external agent in a conservative force field, this work is always equal to change in stored
potential energy of the force field. Based on this concept we can deduce the relation in potential energy
and force.
See the video for details – https://youtu.be/QBM0U-6vkzk
To understand the same with applications of the above logic, see the example videos below –