5.15: Non-inertial Frames of Reference

A reference frame accelerating or decelerating relative to an inertial frame is a non-inertial frame. To help understand this, consider what taking off in an airplane, turning a corner in a car, riding a merry-go-round, and the circular motion of a tropical cyclone all have in common. All these systems are accelerating, decelerating, or rotating relative to the Earth; hence, they all are non-inertial frames. All these systems exhibit inertial forces, which merely seem to arise from motion, because the observer's frame of reference is accelerating or rotating. We can reconcile these points of view by examining the frames of reference used. A physicist will choose whatever reference frame is the most convenient for the situation being analyzed. Physicists have no problem in including inertial forces and Newton's second law, as usual, if that is more convenient. Similarly, non-inertial (accelerated) frames of reference are used when it is helpful. Different frames of reference must be considered, for example, when discussing the motion of an astronaut in a spacecraft traveling at speeds near the speed of light, as this applies to the special theory of relativity.

The Earth can be used as an inertial frame of reference with little or no worry about any effects caused by its rotation. However, such effects do exist, for example, in the rotation of weather systems. Viewed from above the North Pole, the Earth rotates counterclockwise, and any motion in the Earth's Northern Hemisphere experiences a Coriolis force to the right. The opposite occurs in the Southern Hemisphere, where the force is to the left. Because the Earth's angular velocity is small, the Coriolis force is usually negligible, but it has substantial effects for large-scale motions, such as wind patterns. The Coriolis force causes hurricanes in the Northern Hemisphere to rotate counterclockwise, whereas tropical cyclones in the Southern Hemisphere rotate clockwise.

The rotation of tropical cyclones and the path of a ball on a merry-go-round can just as well be explained by inertia and the rotation of the system underneath. When non-inertial frames are used, inertial forces, such as the Coriolis force, must be invented to explain the curved path. There is no identifiable physical source for these inertial forces. When inertial frames are used, inertia explains the path, and there is an identifiable source for every force. We can use either view to describe nature, but a view in an inertial frame is simpler, as all forces have origins and explanations.

This text is adapted from Openstax, University Physics Volume 1, Section 5.6: Common Forces and Section 6.3: Centripetal Force.

Recall that the frames of reference wherein Newton's laws hold true are known as the inertial frames. However, there are frames of reference which defy Newton's laws, called the non-inertial reference frames.

Non-inertial frames are either accelerating or decelerating relative to the inertial frames.

For example, when an airplane takes off, the passengers feel a backward force opposite to the airplane's acceleration. This violates Newton's second law according to which objects are accelerated in the direction of the net external force.

In non-inertial frames, inertial or fictitious forces that have no physical origin are necessary to explain the motion of objects. So, in mechanics, it is more convenient to use an inertial frame.

Ideally, a frame of reference fixed to the Earth is non-inertial due to its revolution and rotation. However, the forces due to the Earth's rotation are negligible in small mechanical motions but affect large-scale motions like wind patterns.

The fictitious force in this frame deflects the wind in the clockwise direction in the northern hemisphere and counterclockwise in the southern hemisphere.