$$\rightleftharpoonup{xx}$$
$$\longleftharp{xx}$$,
$$\longrightharp{xx}$$,
Pseudo forces, or fictitious forces, appear to act on an object in motion in a rotating frame of reference with respect to an inertial reference frame. These forces are not real forces but rather mathematical constructs and are introduced to simplify calculations in a non-inertial frame while using Newton's laws of motion. Common examples of pseudo forces include centrifugal, Coriolis, and Euler forces. These forces are essential in fields such as mechanics, astrophysics, and fluid dynamics, where the motion of objects in non-inertial reference frames is commonly encountered.
Consider a ball tied to a string whirling in a horizontal plane. According to Newton's first law of motion, when observed from an inertial frame of reference, the ball would travel in a straight line. However, the tension in the string provides the centripetal force continuously to keep the ball moving in a circular path. Centrifugal force is not required in this inertial frame as all motion can be adequately described using only real forces and Newton's laws of motion.
Now, consider a frame of reference rotating with the ball around the same axis as the ball. As viewed from this frame, the ball is stationary. However, the tension force in the string or the centripetal force still acts on the ball directed towards the axis of rotation.
This contradicts Newton's laws of motion, according to which the ball must accelerate in the direction of the net applied force, i.e., towards the axis of rotation. Introducing a centrifugal force equal to and opposite to the centripetal force solves the problem. The net force on the ball is zero, which keeps it stationary in the rotating frame of reference.
Fictitious forces are necessary for formulating correct equations of motion using Newton's first two laws. However, the fictitious forces do not obey Newton's third law, which requires that the equal and opposite forces exist in the same frame of reference. This means that centrifugal and centripetal forces are not action and reaction forces.
