An inertial reference frame is a frame of reference in which a body with zero resultant force remains at rest or moves with constant velocity. Therefore, Newton's laws of motion apply without introducing additional apparent forces.
This is an HL-only concept in A.5 Galilean and special relativity.
A reference frame is a coordinate system, together with a method of measuring time, used by an observer to assign positions and times to events. A frame is inertial if it is not accelerating or rotating.
Newton's first law provides the test. If , then , so the body's velocity remains constant:
Any frame moving at constant velocity relative to an inertial frame is also inertial. For example, consider a train moving at a constant velocity of along a straight track. A passenger throws a ball vertically upward. Relative to the train, the ball returns to the passenger; relative to the ground, it follows a curved path. The measured motions differ, but both the train and ground frames can be treated as inertial because neither is accelerating.
| Inertial frame | Non-inertial frame |
|---|---|
| At rest or moving with constant velocity relative to another inertial frame | Accelerating or rotating relative to an inertial frame |
| Newton's laws apply directly | Apparent forces may be required to explain motion |
| Example: a train moving uniformly in a straight line | Example: a car accelerating or turning |
A common misconception is that an inertial frame must be stationary. There is no universal stationary frame: all inertial frames moving uniformly relative to one another are equally valid. This principle underlies both Galilean relativity and Einstein's first postulate of special relativity.
Exam technique: For an Explain question, state that the frame has no acceleration, apply Newton's first law, and conclude that an object with zero resultant force has constant velocity. Do not define an inertial frame merely as “a frame that does not move.”
