In physics, a frame of reference is a coordinate system used to describe the motion and positions of objects. A non-inertial frame of reference refers to a coordinate system that is undergoing acceleration or rotation with respect to an inertial frame of reference.
An inertial frame of reference is a frame that remains at rest or moves with a constant velocity in a straight line. In an inertial frame, Newton's first law of motion holds, which states that an object in motion will continue to move at a constant velocity unless acted upon by external forces.
In contrast, a non-inertial frame of reference is one in which Newton's first law does not hold because there are apparent forces present. These forces are often referred to as "fictitious forces" because they arise due to the acceleration or rotation of the frame, rather than from any physical interactions.
The most common example of a non-inertial frame is an accelerating reference frame, such as an elevator moving upward or a car accelerating. In these cases, an observer within the accelerating frame experiences a sensation of being pushed or pulled, even in the absence of any external forces. This sensation is due to the appearance of fictitious forces, such as the "pseudo-force" of gravity that appears to act in the opposite direction of the acceleration.
Another example of a non-inertial frame is a rotating reference frame, such as the Earth rotating on its axis. In this case, an observer within the rotating frame experiences the Coriolis force, which appears to deflect moving objects to the right or left.
When working with non-inertial frames, additional considerations and mathematical corrections must be taken into account to accurately describe the motion and dynamics of objects within those frames. These corrections often involve introducing fictitious forces or modifying the equations of motion to account for the acceleration or rotation of the frame itself.