Non-Inertial Frames

Formulating the laws of motion in accelerated and rotating non-inertial frames.

General idea of the topic

When motion is described from a frame that accelerates or rotates, Newton's second law no longer holds with the real forces alone. To keep using the same equation, inertial terms are added, the fictitious forces, which have no agent or reaction but do have measurable effects for that observer: the backward push on a car that starts off, the force throwing you outward on a bend or the deflection of winds.

This block deals with the general idea of a fictitious force, the centrifugal force that appears in a rotating system, the general rotating frame, which combines translation and rotation in a single relation, and the Coriolis force, which acts on bodies moving within a rotating system.

What the student is expected to understand

By the end, the student should be able to set up the dynamics in a non-inertial frame by adding the right inertial forces and check the result by describing the same motion from an inertial frame.

The student should also know why these forces are called fictitious and why, even so, an observer inside the frame feels and measures them.

Recommended learning route

1. Fictitious Forces: introduces inertial forces, how they are obtained and how they are interpreted.
2. Centrifugal Force: studies the force that appears in a rotating system, its expression and everyday examples.
3. General Rotating Frame: brings translation and rotation together in a single relation and separates the terms of the absolute acceleration.
4. Coriolis Force: covers the Coriolis force, which depends on the relative velocity, and its effects on the atmosphere and the oceans.

Physical criterion to acquire

The essential criterion is to decide which observer is used and not to mix descriptions. In an inertial frame there are no fictitious forces; in a non-inertial one they are added and treated as additional forces. The acceleration of the frame and the fictitious force that compensates it are never added together. Checking the result from the other point of view avoids double counting.

Connection with real problems

• vehicles starting, braking or taking bends.
• centrifuges and rotating rides.
• atmospheric circulation and ocean currents.
• rotating devices and inertial navigation.

Final goal of the topic

The final goal is to solve problems from a non-inertial frame with the correct inertial forces and to interpret their physical effect without confusing them with real interactions.