A.5.1 (HL)—Reference frames
- Syllabus
- First assessment 2025
- Objective
- —
- Level
- HL
Choose a Reference Frame
HL onlyDefine the frame
A reference frame is a coordinate system, with a chosen origin and axes, together with a way of assigning time to events. Position and time are coordinates: they describe an event only after the observer’s frame has been stated.
Describe the same event in two frames
For an event, record its position x and time t in frame S, then x′ and t′ in frame S′. If S′ moves at constant velocity relative to S, both frames are inertial. The event is the same physical occurrence even though its coordinates may differ.
Check the frame type
An inertial reference frame is non-accelerating. Newton’s laws can be used in their usual form in such a frame. If the frame accelerates or rotates, extra apparent forces may be needed and it is not an inertial frame for this syllabus treatment.
Common trap
A frame is not just a camera viewpoint. It specifies the spatial axes and the time measurement used to assign coordinates; therefore “at rest” or “moving” has meaning only relative to a stated frame.
A.5.1 (HL) Exam Analysis
HL onlyAssessment in practice
1–2 marksHow it is assessed
The evidence tests whether you can identify a frame of reference and explain why an observer or object is at rest in a chosen frame. The scoring focus is the absence of relative velocity or change in position, plus an explicit position-and-time coordinate description when a definition is requested.
Command terms
State / Define / Explain
What earns marks
State the reference frame before interpreting motion. Define the spatial origin and time coordinate, identify the observer or object at rest in the frame, and use relative motion consistently. For a definition question, include both coordinates/axes and the time measurement.
Watch for
Describing a frame as only a visual viewpoint without mentioning coordinates and time.
Representative question
Question 1
[Maximum number: 1]
Explain why observer Y is at rest in the reference frame of the electron.
there is no relative velocity/change in position between Y and the electron OR
both move at the same velocity
Retrieve the A.5 Galilean and Special Relativity Model
HL onlyChoose the model
State the inertial reference frame first. Galilean relativity uses x′=x−vt, t′=t and u′=u−v. Special relativity uses the two postulates, Lorentz transformations and u′=(u−v)/(1−uv/c²).
Track what changes and what is invariant
In special relativity, use γ=1/√(1−v²/c²), the invariant interval (Δs)²=(cΔt)²−(Δx)², proper time, proper length, Δt=γΔt0 and L=L0/γ. Separate measurements of space and time can change between frames, while the interval and vacuum light speed do not.
Read the evidence
On a space–time diagram, world-line angle gives tanθ=v/c, frame axes determine simultaneity, and no world line exceeds the light line. Muon survival provides experimental evidence: time dilation explains the longer Earth-frame lifetime, while length contraction explains the shorter atmospheric distance in the muon frame.
Final retrieval check
For every calculation, identify the frame, select the proper quantity if one is given, keep signed velocities and units consistent, and check the result against c, γ≥1, or the invariant interval. The syllabus requires applying the transformations and equations, not deriving them.