Inertial and non-inertial frames
A non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame. Anaccelerometer at rest in a non-inertial frame will in general detect a non-zero acceleration. In a curved spacetime all frames are non-inertial. All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration. Measurements in one inertial frame can be converted to measurements in another by a simple transformation .
The motion of a body can only be described relative to something else—other bodies, observers, or a set of space-time coordinates. These are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary. For example, suppose a free body that has no external forces on it is at rest at some instant.
In an inertial frame, Newton's first law, the law of inertia, is satisfied: Any free motion has a constant magnitude and direction. Newton's second law for a particle takes the form
F = ma
with F the net force (a vector), m the mass of a particle and a the acceleration of the particle (also a vector) which would be measured by an observer at rest in the frame.
In measurements made with respect to some other frames of reference, Newton's laws appear to be violated. If you try throwing and catching balls on a merry-go-round, you'll also observe some apparent violations of Newton's laws.
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