In this course, you have worked with the 3 central principles to mechanics, the momentum principle, the energy principle, and the angular momentum principle. These 3 principles can predict or explain all motion in the universe as we know it. They are incredibly powerful principles that have been tested in many experiments. In this last set of notes, you will be reminded of them.

The momentum principle describes how the momentum of a system will change as a result of external forces. It is a vector principle as it describes how an system will move in three dimensions.

$$\Delta \vec{p}_{sys} = \vec{F}_{ext} \Delta t$$

If the system is chosen such that there are no external forces, or it is the case the external forces can be neglected, the momentum of the system is conserved.

$$\Delta \vec{p}_{sys} = 0 \longrightarrow \vec{p}_{sys,i} = \vec{p}_{sys,f}$$

The energy principle describes how the energy of a system will change as a result of external work and energy exchange due to a temperature difference. It is a scalar principle as it describes how energy is transferred in and out as well as around a system in different forms.

$$\Delta E_{sys} = W + Q$$

If the system is chosen such that there are no exchanges of energy with the surroundings, or it is the case these exchanges can be neglected, the energy of the system is conserved.

$$\Delta E_{sys} = 0 \longrightarrow E_{sys,i} = E_{sys,f}$$

The angular momentum principle describes how the angular momentum of a system will change as a result of external torques. It is a vector principle as it describes how a system will rotate or translate in 3 dimensions.

$$\Delta \vec{L}_{sys} = \vec{\tau}_{ext} \Delta t$$

If the system is chosen such that there are no external torques, or it is the case these external torques can be neglected, the angular momentum of the system is conserved.

$$\Delta \vec{L}_{sys} = 0 \longrightarrow \vec{L}_{sys,i} = \vec{L}_{sys,f}$$