Right now you feel perfectly still — yet you’re spinning with the Earth and racing around the Sun at tens of kilometres a second. So are you moving or not? The honest answer is: it depends who’s asking. A reference frame is simply the point of view you measure motion from, and getting comfortable with it is the first step into the whole world of relativity.
📘 What you need to know
A reference frame is a set of coordinates used to record the position and time of events
It’s the point of view from which an object, at a specific coordinate, is at rest
The word relative tells you which point of view a measurement is taken from
Velocity and direction of the same object can differ between two frames
An inertial frame is one that is not accelerating (moving at constant velocity, or at rest)
All inertial frames move at constant velocity relative to each other
There is no absolute reference frame — nothing in the Universe is truly stationary
What is a reference frame?
In physics we constantly need to be clear about whose point of view we mean. That’s what the word relative does. The velocity of a car relative to someone standing still is different from the velocity of that same car measured by a driver cruising alongside it at matching speed.
A reference frame (or frame of reference) is the point of view we attach to those measurements. Formally:
Reference frame — definition
A set of coordinates used to record the position and time of events
Here’s the trick to remembering it: a reference frame is wherever you are sitting still. If you’re reading this at a desk, that desk is your reference frame. You feel stationary — even though the Earth is spinning on its axis and orbiting the Sun the whole time. A reference frame is the point of view where an object, at its own coordinate, is at rest.
Think of it like sitting on a train and watching a coffee cup on your table. To you, the cup isn’t moving at all — it’s sitting still. To someone on the platform watching the train fly past, that same cup is doing 120 km/h. Neither of you is wrong. You’re each just measuring from your own frame.
Everyday examples
The simplest example is direction. Imagine a car driving down a road with two people standing on opposite sides. One person sees the car move to their right; the person facing them sees it move to their left. Both are completely correct — they’re just describing the motion from different points of reference.
The same car, two reference frames. Person A and Person B disagree on the direction — and both are right, because each measures relative to themselves.
A train leaving a station gives an even sharper example. Person A stands on the platform; Person B sits on the train. As the train pulls away, Person A sees themselves as still and Person B gliding off to the right. But Person B feels perfectly still too — from their seat, it’s Person A and the whole platform that appear to slide to the right. Each person is stationary in their own frame and sees the other one moving.
Quick recap: A reference frame is the point of view you measure from. In your own frame you are always at rest, and everything else is described relative to you.
Inertial frames of reference
There’s one special, well-behaved type of frame that the whole of relativity is built on: the inertial reference frame.
Inertial reference frame — definition
A non-accelerating reference frame
In plain words, an inertial frame is one that is either at rest or moving at a constant velocity — steady speed, straight line, no acceleration. All inertial frames move at constant velocity relative to one another. This matters because anything moving in a curved path is accelerating, so you’ll only ever deal with frames moving in straight lines at steady speed.
Constant velocity in a straight line is an inertial frame. Any curved or turning path involves acceleration — not inertial. You’ll only meet inertial frames in the exam.
One more big idea: there is no absolute reference frame in the Universe. There’s no single place that is truly, completely stationary for everything else to be measured against. Everything is always moving relative to something else — motion only ever has meaning relative to a chosen frame.
Why does this matter so much? Because “no absolute frame” is the seed of everything to come. Since no frame is the special, correct one, the laws of physics have to work exactly the same in every inertial frame. Hold onto that thought — it grows into Galilean relativity, and later into Einstein’s postulates.
Stationary and moving frames
To do calculations later, we give the two frames names. We label the stationary frame S, with coordinates (x, y, t). A second frame moving relative to it is S′, with coordinates (x′, y′, t′). The little prime mark (′) always tags the moving frame.
Picture Person C standing still while Person D glides past at velocity v, and a balloon pops off in the distance. Person C measures the pop at one distance; Person D, moving, measures it at another. Same event, two frames, two numbers.
Frame S (stationary, observer C) and frame S′ (moving at v, observer D). The prime always marks the moving frame. The same balloon pop is recorded at a different distance in each.
Frame S stationary (x, t)
moving at v
Frame S′ moving (x′, t′)
Worked examples
These are the classic “who measures what” questions. The maths is tiny — the whole skill is deciding who is stationary, who is moving, and whose point of view the answer is measured from.
WE 1
A student cycles to school at 7.5 m s−1 (measured by their aunt, who is standing still at a bus stop). A friend cycles exactly in line beside them at the same speed. At what speed does the friend measure the student to be moving?
Step 1 — use the friend’s frame
The friend is stationary in their own frame.
Step 2 — student’s speed relative to friend7.5 − 7.5 = 00 m s⁻¹Cycling in line, the friend sees the student sitting perfectly still beside them.
WE 2
A person walks at 1.4 m s−1 along a moving airport walkway. The walkway itself moves at 0.6 m s−1 (measured by a stationary observer). How fast does the stationary observer see the person moving?
Step 1 — same direction, so speeds add
walkway speed + walking speed
Step 2 — substitute0.6 + 1.4 = 2.02.0 m s⁻¹The walkway carries them along, so the person covers ground faster than they walk.
WE 3
Two trains taxi past each other on parallel tracks. Train A moves due north at 22 m s−1 and Train B moves due south at 16 m s−1, both measured from the ground. How fast does Train A move relative to Train B?
Step 1 — set north as positive
Train A = +22, Train B = −16
Step 2 — subtract B’s velocity22 − (−16) = 22 + 16 = 3838 m s⁻¹ northBecause they move in opposite directions, the closing speed is the sum — watch those signs!
WE 4
A train moves at 18 m s−1 past a platform. A child walks along the train at 1.5 m s−1 in the direction of travel for 12 s. How far does the child move according to (a) an observer on the train, and (b) an observer on the platform?
(a) Observer on the train (same frame as child)
distance = speed × time
= 1.5 × 12 = 18 m(b) Observer on the platform
add the distance the train itself moved:
= 18 + (18 × 12) = 18 + 216234 mThe train observer shares the child’s frame, so uses plain speed × time. The platform observer must add the train’s motion too.
🛠️ Tackling a reference-frame question
Spot the frames. Who is stationary (frame S) and who is moving (frame S′)?
Whose answer? Read the wording — “relative to…”, “in the frame of…”, “measured by…” tells you the point of view.
Same frame? If the event happens in the observer’s own frame, use ordinary physics (no conversion).
Different frame? You’ll need to combine velocities — add for same direction, subtract for opposite.
Mind the sign. Pick a positive direction first, then plug in.
💡 Top tips
You are always at rest in your own frame. Every measurement is made relative to the observer.
Watch the keywords. “Relative to”, “in the frame of”, and “measured by” all point to a specific frame.
Prime = moving. The (′) mark always tags the moving frame S′.
No frame is special. There’s no absolute “still” frame — only frames relative to each other.
Sketch it. A quick drawing with the velocities labelled saves you from sign slips.
⚠ Common mistakes
Assuming there’s one “correct” frame — both observers are equally valid
Forgetting direction: velocity is a vector, so opposite directions need a minus sign
Adding the frame’s velocity when the event is measured within the observer’s own frame
Confusing which frame gets the prime — the prime is always the moving frame
Thinking accelerating (curved, turning) frames appear in the course — only inertial frames do
Quick recap: A reference frame is the coordinate system you measure from, where you are at rest. Inertial frames don’t accelerate and move at constant velocity relative to each other. No frame is absolute, so the same motion can look different — and every observer is right within their own frame.
You’ve just laid the foundation stone of relativity. Next we build straight on top of it: if no frame is special, then the laws of physics must be identical in all of them — that’s Galilean relativity, where we’ll turn these “who sees what” ideas into proper transformation equations for swapping between frames. See you there.
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