A reference frame is a coordinate system associated with a reference object (reference body) and a clock, allowing the position of an object to be located and its motion to be described. Motion is always relative to the chosen reference frame.
Discover FizziQ
How to measure it in class
With the FizziQ app, it is possible to explore the relativity of motion.
Steps:
- Measure the speed of an object with GPS in the terrestrial reference frame
- Film an object from another moving object (e.g., ball thrown in a train)
- Compare the observed motion from different points of view
- Use the accelerometer to detect changes in reference frame
- Observe that the absolute acceleration is zero in a Galilean reference frame in uniform motion
Scientific activities on this topic
- Relative motion in a car
- Study of motion in a carousel: https://www.fizziq.org/en/activities/centrifuge/
- Fall of a ball filmed from a moving cart
Learn more
Common reference frames:
| Reference Frame | Reference Body | Use |
|---|---|---|
| Terrestrial | Earth’s surface | Everyday motions |
| Geocentric | Earth’s center | Satellites, GPS |
| Heliocentric | Sun’s center | Planetary motions |
| Laboratory | Table, room floor | Lab experiments |
Relativity of motion:
A passenger seated in a train is:
- Stationary in the train’s reference frame
- In uniform rectilinear motion in the terrestrial reference frame
- In complex motion in the heliocentric reference frame
Galilean reference frame:
A Galilean reference frame is a reference frame in which the principle of inertia is verified (an isolated object maintains uniform rectilinear motion). The terrestrial reference frame is approximately Galilean for short-duration experiments.
Inertial forces:
In a non-Galilean (accelerated) reference frame, fictitious forces must be added: centrifugal force in a rotating reference frame, inertial force in an accelerating reference frame.
Formula
Composition of velocities (Galilean case):
v(M/R) = v(M/R’) + v(R’/R)
where:
- v(M/R): velocity of M in reference frame R
- v(M/R’): velocity of M in reference frame R’
- v(R’/R): velocity of R’ relative to R
Application examples
- A passenger walks at 5 km/h in a train traveling at 100 km/h: their ground speed is 105 km/h (or 95 km/h if walking backward)
- The Earth rotates on its axis at 1670 km/h at the equator (geocentric reference frame)
- An object dropped in a free-falling elevator appears to float (elevator reference frame)
- GPS must account for satellite motion relative to the ground
FAQ
Q: Why isn’t the terrestrial reference frame truly Galilean? A: The Earth rotates on its axis and around the Sun. These rotations create centripetal accelerations. But for short, local experiments, these effects are negligible.
Q: Can I measure the reference frame with FizziQ? A: FizziQ’s accelerometer measures acceleration in the smartphone’s reference frame. If the acceleration is zero (excluding gravity), the smartphone is in a Galilean reference frame.
Q: How do you choose the right reference frame? A: Choose the reference frame that most simplifies the problem. To study a fall, the terrestrial reference frame is appropriate. To study a satellite, the geocentric reference frame is preferable.
Related concepts
Kinematics - Relative motion - Galilean reference frame - Acceleration - Composition of velocities - Inertial force