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Mathematics for Physics

170 Inertial Frame

A reference frame in which Newton’s first law holds that is used to state the laws of mechanics without fictitious forces from acceleration of the axes.

The law of inertia as a frame test. An inertial 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.

Einstein synchronization. Clocks at different locations in an inertial frame can be synchronized with light signals. Synchronization is the procedure that sets distant clocks to a common time. This principle is used to define one coordinate time throughout the frame.

Note: Also called an inertial reference frame.

170.1 References

  1. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — source for the heading explanation.
  2. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — inertial reference frame as one where Newton’s first law is valid.
  3. Griffiths, D. J. Introduction to Electrodynamics. Cambridge University Press, 2024. — inertial frame as one in which Newton’s first law holds.
  4. Emam, M. H. Covariant Physics. Oxford University Press, 2021. — inertial frames as constant-velocity axes preserving Newton’s law.
  5. Carroll, S. M. Spacetime and Geometry. Cambridge University Press, 2021. — synchronization of clocks in an inertial frame.