Coriolis Force on Particle Motion

As was pointed out earlier, when we have considered the physical principles of the ballistic gravimeter and the pendulum an influence of the Coriolis force was ignored. Now we will try to take into account this factor and consider the motion of a particle near the earth s surface. With this purpose in mind let us choose a non-inertial frame of reference, shown in Fig. 3.5a its origin 0 is located near the earth s surface and it rotates together with the earth with angular velocity a . The unit vectors i, j, and k of this system are fixed relative to the earth and directed as follows i is horizontal, that is, tangential to the earth s surface and points south, j is also horizontal and points east, k is vertical and points upward. As is shown in Fig. 3.5a SN is the earth s axis, drawn from south to north, I is the unit vector along OiO, and K is a unit vector parallel to SN. 

we derive again but in a slightly different way than in Chapter 2 the equation of a motion in a non-inertial frame of reference. As before, r is the position of the moving particle with respect to 0 and OiO = ro. The position of the particle with respect to the origin 0i of the inertial frame is 

Performing a differentiation with respect to time twice, we obtain the acceleration in the inertial system 

Here fo is the acceleration of the origin 0, and since 0 moves in a circle with constant angular velocity co = coK, we have 

Now we find the relationship between forces and the function f and with this purpose in mind we make use of Equations (3.62-3.64). They give 

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