Centrifugal force

We have managed to arrive so far without mentioning the term centrifugal force. This is rather curious because centrifugal force is a term in everyday use, while centripetal force is hardly known except to the student of mechanics.

Consider again the stone rotating, on a table, in a horizontal circle. We have established the fact that there is an inward force on the stone, exerted by the string, for the set purpose of providing the acceleration towards the centre – yes, centripetal force, however unknown it may be, is a real, practical, physical force. But is there also an outward force?

The situation is similar to that of the accelerating aircraft towing a glider that we described earlier. There is an outward reaction force on the outer end of the string caused by the fact that it is accelerating the stone inwards: an inertia force, and we could call this a centrifugal reaction force. This keeps the string in tension in a state of equilibrium just as if it were tied to a wall and pulled. Note, however, that there is no outward force on the stone, only an inward one applied by the string to produce the centripetal acceleration. As with the accelerating glider described previously and shown in Fig. 1.2, the forces on the two ends of the string are in balance, but the forces on the object, the stone or the glider are not, and hence acceleration occurs.

The concept of inertia forces is a difficult one. In a free-body diagram of the horizontally whirling stone, the only externally applied horizontal force is the inward force applied by the string. This force provides the necessary accelera­tion. There may be outward forces on the internal components of the system like the string, but not on the overall system. Note that if you let go of the string, the stone will not fly outwards, it will fly off at a tangent.

To sum up motion on curved paths. There is an acceleration (v2/r) towards the centre, necessitating a centripetal force of miP-lr.

At this stage, the reader is advised to try some numerical questions on motion on curved paths in Appendix 3.