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Mathematics for Physics

171 Inertial Reference Frames

A coordinate system in which a free particle with no external forces stays at rest or moves in a straight line at constant speed.

The law of inertia as a frame test. An inertial reference frame is a frame in which Newton’s first law holds. Newton’s first law is the statement that a body with no net force keeps constant velocity. This principle is used to test whether a given coordinate system is inertial.

Closure under constant-velocity boosts. A frame that moves at constant velocity relative to an inertial frame is itself inertial. Constant velocity is a speed and direction that do not change with time. This principle is used to generate the family of frames in which the laws of mechanics keep the same form.

The absence of fictitious forces. In an inertial frame every acceleration comes from a real force. A real force is a push or pull from an identifiable contact or field. This principle is used to apply Newton’s second law with no extra correction terms.

Note: Also called an inertial frame. See Inertial Frame.