Forces of Inertia in Rotating Frame of Reference

Fig. 1.26

Let’s consider an example of a non-inertial frame of reference which is the rotating frame of reference.

Take a round disk of a radius rotating uniformly at an angular velocity = const around the vertical axis through its center . Consider a small ball of a mass , whirling around on the end of a string, which is tied to a rigid point at O, along the edge of the disc at a velocity relative to it. (Fig. 1.26).

Two observers analyse the motion of the small ball. One of them is on the immobile axis, or in the inertial frame of reference . The other observer is on the disc near its centre and rotates together with it, this observer is in the non-inertial frame of reference .

For the observer in frame the motion of the ball is a uniform circular motion with . The observer in also swatches the uniform circular motion of the ball, but the speed is .

The acceleration of the ball in is

Here is the acceleration of the ball relative to the disc, i.e., in the non-inertial frame of reference .

Evaluate the centripetal acceleration in non-inertial frame of reference:

Multiplying both parts of this equation by mass of the particle we will get:

;

.

The observer on the disc, or in the frame concludes, that in addition to the 'real' force of tension of the thread, , there are two other forces acting on a small ball:

— the centrifugal force or ;

— the force of Coriolis or .

Let us consider each of these forces in detail.

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