Contents

3.12 The Coriolis Force 45operates perpendicular to the object’s direction of motion. The centripetal force (perunit mass), which is a true force, is given by:Centripetal force =−Ω 2 r (3.31)where r is the object’s distance from the centre of the turntable, and Ω = 2π/Tis the rotation rate with T being the rotation period. Per definition the rotation rateΩ is positive for anticlockwise rotation and negative for clockwise rotation. Whenreleasing the object, it will fl away on a straight path with reference to the f xedframe of reference.In the rotating frame of reference, on the other hand, the object remains at thesame location and is therefore not moving at all. Consequently, the centripetal forcemust be balanced by another force of the same magnitude but acting in the oppositedirection. This apparent force – the centrifugal force – is directed away from thecentre of rotation. Accordingly, the centrifugal force is given by:Centrifugal force =+Ω 2 r (3.32)When releasing the object, an observer in the rotating frame of reference will seethe object flyin away on a curved path – similar to that shown in Fig. 3.12.3.12.3 Derivation of the Centripetal ForceThe speed of any object attached to the turntable is the distance travelled over a timespan. Paths are circles with a circumference of 2πr, where r is the distance from thecentre of rotation, and the time span to complete this circle is the rotation period.Accordingly, the speed of motion is given by:v = 2π Tr = Ωr. (3.33)During rotation, the speed of parcels remains the same, but the direction ofmotion and thus the velocity changes (Fig. 3.14). The similar triangles in Fig. 3.14give the relation δv/v = δL/r. Since δL is given by speed multiplied by time span,this relation can be rearranged to yield the centripetal force (per unit mass):dvdt=− v2r , (3.34)where the minus sign has been included since this force points toward the centre ofrotation. Equation (3.31) follows, if we finall insert (3.33) into the latter equation.