Fictitious Forces

Inertial fictitious forces introduced in accelerated frames to apply Newton's laws.

General idea of the topic

A fictitious force is the term that must be added to the second law for it to keep holding in an accelerating reference frame. It has the form of minus the mass times the acceleration of the frame, no body produces it and therefore it has no reaction. Even so, for the accelerated observer it acts as one more force: it pushes, deforms and can be measured.

The topic explains why they appear, how their expressions are obtained and how to interpret them without falling into two opposite mistakes: treating them as real interactions or denying them any physical effect for whoever feels them.

What the student is expected to understand

By the end, the student should be able to write the fictitious force corresponding to a frame with known acceleration and use it to solve, from inside, problems such as the pendulum in an accelerating carriage.

The student should also be able to check the result by describing the same motion from an inertial frame, where that force does not appear.

Recommended learning route

1. Concept of Fictitious Forces: starts from Newton's law in an accelerating frame and from the expression of the inertial force.
2. Interpretation of Fictitious Forces: discusses what it means for a force to be fictitious, when it is convenient to use it and why it must not be drawn in an inertial frame.

Physical criterion to acquire

The essential criterion is that fictitious forces belong to the description of the accelerated observer, not to the interactions of the problem. They are added only if working in that frame and never together with the inertial description: using both at once counts the same effect twice.

Connection with real problems

• vehicles accelerating seen from inside.
• pendulums and hanging objects in a carriage or an elevator.
• elevators: apparent weight.
• rockets and spacecraft during maneuvers.

Final goal of the topic

The final goal is to set up and solve problems from an accelerating frame with the correct fictitious force and to interpret it without confusing it with a real interaction.