Question: Under what conditions does the energy equation for the point particle system differ from the energy equation for the extended system? Give two examples of such a situation. Give one example of a situation where the two equations look exactly alike.

The types of kinetic energy are described as the translational and the rotational kinetic energy.

The energy principle states that energy is neither created nor destroyed, only converted from one form to another.

The point particles will only consist of translational kinetic energy. Therefore, the extended systems will have different energy equations if energy change occurs between them. However, the conditions for the energy for the point particle system and the extended system will differ if the extended system has elastic, chemical, internal and thermal energy. Moreover, if the extended system rotates, the equation can also be different if the point does not move with the application of normal force.

The two examples of the system are a person running uphill and a disk rotating down an inclination. In the first example, the internal energy is not considered, and in the second example, the rotational kinetic energy is not considered.

The one example of a situation where the two equations look exactly alike is an object that is freely falling and not rotating. However, if the extended system is considered in this example, only the translational kinetic energy changes, which is the only energy that changes for the system of a point particle. Hence, the two equations will be the same in this condition.

Thus, the two examples of such a situation in which the point particle system's energy equation differs from the extended system's energy equation are a person running uphill and a disk down the incline.