The concept of an inertial frame of reference.

The idea

An inertial frame of reference is a coordinate system in which a body with no resultant force acting on it remains at rest or moves with constant velocity in a straight line. In such a frame, Newton’s first law holds, so any acceleration observed must be caused by a real resultant force rather than by the frame itself accelerating. For example, a laboratory bench fixed to the ground is approximately inertial for short experiments, whereas a bus braking sharply is not: a loose object appears to lurch forward even though no forward force acts on it. Identifying inertial frames matters because the laws of physics, including Einstein’s postulates, are stated with respect to them, and because observers in different inertial frames may disagree about simultaneity and measured lengths and times.

What earns the marks

• Defines an inertial frame as one in which Newton’s first law is obeyed, so a body with zero resultant force has zero acceleration.
• Explains that a non-inertial frame is accelerating or rotating, producing apparent forces that are not caused by physical interactions.
• Uses a concrete example, such as a laboratory approximately at rest relative to the ground, to distinguish inertial from non-inertial frames.
• States that inertial frames move at constant velocity relative to one another, so no inertial frame is absolutely privileged.
• Links the concept to special relativity by noting that the postulates are asserted for all inertial frames.
• Recognises that real frames are only approximately inertial when accelerations are small compared with the precision of measurement.

Common mistakes and how to put them right

• Treating any frame at rest as inertial while ignoring that a frame accelerating in a straight line is non-inertial.

  Put it right: Test whether Newton’s first law holds for a free body in that frame.

• Assuming that a rotating frame such as the Earth’s surface is exactly inertial.

  Put it right: Describe it as approximately inertial and to note that rotation produces small apparent effects such as the Coriolis effect.

• Confusing an inertial frame with a frame in which objects are stationary.

  Put it right: Inertial frames may move at any constant velocity, and only acceleration of the frame breaks inertia.

Exam tips

• Define the frame by the behaviour of a free body, not by whether the observer feels motion.
• When a question describes a lift, train or rotating platform, state explicitly whether the frame is inertial and justify this with the resultant force on a free test object.
• Use the phrase constant velocity in a straight line rather than constant speed alone, because direction matters.