Reference Frames (Dynamics › Fundamentals)

Inertial and non-inertial frames of reference in formulating physical laws.

General idea of the topic

A reference frame is the observer and the axes from which a motion is described. Newton's laws hold as they stand in inertial frames, which neither accelerate nor rotate relative to the distant stars. From an accelerating frame the same motion obeys other equations, in which terms appear that correspond to no real interaction.

This topic establishes what an inertial frame is, what changes when moving to one that accelerates, and how the accelerations measured by two observers are related. It is the basis for understanding fictitious forces later.

What the student is expected to understand

By the end, the student should be able to decide whether a frame is inertial from its motion, transform positions and accelerations between two frames, and explain why a passenger sees an object accelerate without any real force pushing it.

The student should also be able to relate the acceleration measured by one observer to the one measured by another when there is no relative rotation between their frames.

Recommended learning route

1. Inertial Frames: defines inertial frames, Galilean relativity and the conditions under which Newton's laws hold.
2. Introduction to Non-Inertial Frames: presents what happens in an accelerating frame and why terms appear that are interpreted as fictitious forces.
3. Relative Acceleration: relates the acceleration of a body measured in two different frames.

Essential physical criterion

The essential criterion is to decide, before applying Newton's laws, whether the reference frame is inertial. If it is not, the equations must be corrected or the frame changed; applying the second law as it stands in an accelerating frame produces a result that seems reasonable and is wrong.

Connection with real problems

• vehicles that accelerate or brake, seen from inside.
• elevators and rotating rides.
• navigation and motion on Earth.
• passing between observers in relative-motion problems.

Final goal of the topic

The final goal is to choose the appropriate reference frame, recognise whether it is inertial and correctly relate the descriptions of motion by two observers.