Frame of Reference

Understanding coordinate systems and reference frames for describing motion

2 min read

What is a Frame of Reference?

A frame of reference is a coordinate system that we use to describe the position and motion of objects. Think of it as your “point of view” for observing motion.

Simple Analogy
When you’re sitting in a moving train, you see a person standing on the platform moving backward. But someone on the platform sees you moving forward. Both observations are correct—in different frames of reference!

Types of Reference Frames

1. Inertial Frame of Reference

An inertial frame is one in which Newton’s laws of motion hold true.

Characteristics:

  • The frame is either at rest or moving with constant velocity
  • No acceleration of the frame itself
  • Objects at rest remain at rest (Newton’s 1st Law applies)

Examples:

  • A room at rest on Earth (approximately)
  • A train moving at constant speed on straight tracks
  • A spaceship far from any gravitational influence

2. Non-Inertial Frame of Reference

A non-inertial frame is an accelerating frame where Newton’s laws don’t directly apply.

Characteristics:

  • The frame is accelerating (changing speed or direction)
  • Pseudo forces appear to act on objects
  • Newton’s laws require modification

Examples:

  • A car taking a turn
  • An elevator accelerating up or down
  • A merry-go-round

Pseudo Forces

In non-inertial frames, we introduce pseudo forces (also called fictitious forces) to apply Newton’s laws.

$$\vec{F}_{pseudo} = -m\vec{a}_{frame}$$

where $\vec{a}_{frame}$ is the acceleration of the non-inertial frame.

Example: Elevator

When an elevator accelerates upward with acceleration $a$:

  • You feel heavier
  • Effective weight = $m(g + a)$

When the elevator accelerates downward:

  • You feel lighter
  • Effective weight = $m(g - a)$
Key Point
Pseudo forces are not real forces—they arise because we’re observing from an accelerating frame. They have no third-law reaction pair.

Interactive Demo: Visualize Motion in Different Frames

Explore how motion appears different from various reference frames.

Choosing the Right Frame

The choice of reference frame can simplify problem-solving:

SituationBest Frame to Use
Ground-based problemsEarth’s surface (inertial)
Problems inside vehiclesVehicle frame + pseudo forces
Relative motion problemsOne object as reference

Practice Problem

Check Your Understanding

A person in a lift feels their weight to be $1.2$ times their actual weight. If $g = 10 \text{ m/s}^2$, find the acceleration of the lift.

Solution:

  • Apparent weight = $m(g + a) = 1.2mg$
  • Therefore: $g + a = 1.2g$
  • $a = 0.2g = 2 \text{ m/s}^2$ (upward)