Fundamentals (Dynamics)

Foundational principles of Newtonian dynamics and concepts of mass and inertia.

General idea of the topic

The fundamentals of dynamics answer a question that comes before any calculation: how force relates to motion. Newton's laws give the answer, but they hold only in inertial reference frames and require a good force diagram to be applied. That is why this block brings together the laws, the reference frames and the diagrams.

Each part supports the others. Diagrams turn a real situation into a set of vectors; the laws say what relation those vectors have with the acceleration; and reference frames clarify from where the motion is observed and when the laws can be used as they stand.

What the student is expected to understand

By the end, the student should be able to isolate a body, draw the forces acting on it and write the second law by components in the appropriate reference frame.

The student should also be able to explain why a body with no net force need not be at rest, and what changes when the observer accelerates.

Recommended learning route

1. Newton's Laws: states inertia, the relation between force, mass and acceleration, and action and reaction, with the conditions of each law.
2. Reference Frames: clarifies which reference frames are inertial, how the description changes in an accelerating one and what acceleration each observer measures.
3. Force Diagrams: teaches how to identify the real forces, draw the free body and project onto axes before applying the laws.

Essential physical criterion

The essential criterion is not to write any equation before deciding the system, the reference frame and the real forces acting on it. Newton's law applied to badly identified forces, or in an accelerating frame without correction, gives a result that looks coherent and is false in practice.

Connection with real problems

• motion of vehicles, elevators and projectiles.
• equilibrium of structures and suspended loads.
• analysis of collisions and multi-body systems.
• the basis of the rest of classical mechanics.

Final goal of the topic

The final goal is to set up the dynamics of any body rigorously: choose the reference frame, draw the force diagram, apply Newton's laws and interpret the result.