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An inertial frame of reference is a reference frame where Newton's first law holds valid. In this frame, an object at rest remains at rest, or an object moving at constant velocity continues moving at that velocity when no net force acts on it. A reference frame moving at constant velocity relative to an inertial frame is also inertial.

When a car stops suddenly, the passenger experiences a forward push due to inertia, not an actual force. The passenger's velocity relative to Earth is maintained by Newton's first law. Although the passenger moves forward relative to the car, her motion relative to the Earth-based inertial frame remains constant until friction or another force acts on her.

Earth's surface is not a true inertial frame because Earth rotates and revolves around the Sun, causing acceleration relative to the fixed stars. However, for most practical problems, a reference frame attached to Earth's surface serves as a sufficiently accurate approximation to an inertial frame because the acceleration is relatively small (less than 3.4 × 10⁻² m/s²).

Scientists identify an inertial frame by testing whether Newton's first law applies. If an object's velocity relative to a given frame remains constant when the net force is zero, that frame is inertial. A reference frame at rest relative to the fixed stars is inertial, and all frames moving uniformly with respect to this fixed-star frame are also inertial.

Yes, all inertial frames are equivalent as far as the laws of nature are concerned. No particular inertial frame is more special than another. When analyzing a physics problem, scientists choose one inertial frame over another simply based on convenience and which frame makes calculations easiest.

A non-rotating reference frame attached to the Sun is inertial for all practical purposes because its velocity relative to the fixed stars does not vary by more than one part in 10¹⁰. This extremely small variation is negligible for most physics calculations, making the Sun's frame an excellent approximation of a true inertial frame.

Inertia is the tendency of an object to maintain its velocity, which is the physical basis for defining inertial frames. An inertial frame is precisely one where this inertial property holds true: objects maintain constant velocity when no net force acts on them. This relationship between inertia and inertial frames is central to Newton's first law application.