88, 89] 



EXPERIMENTAL VERIFICATION. 



271 



Fig. 84. 



89. Symmetrical Top. Constrained Motion. While we 

 have in the preceding section considered the very interesting and 

 instructive question of the motion of the most 

 general rigid body under the action of no forces, 

 by far the most frequent case under the practical 

 conditions of experiment is that in which the body 

 is dynamically symmetrical about an axis, that is, 

 the ellipsoid of inertia is of revolution. Such a 

 body we shall call a symmetrical top. This will 

 include not only all ordinary tops and gyroscopes, 

 as well as flywheels, rolling hoops, billiard balls, 

 but even the earth and planets. Suppose such a 

 body to be spinning under the action of no forces, 

 about its axis of symmetry. We have seen that it will remain so 

 spinning, and the angular momentum will have the direction of the 

 axis of symmetry. If now the axis 

 of symmetry OF (Fig. 84), is to 

 move to some other position, OF 1 , 

 which is then to coincide with the 

 new instantaneous axis, the angular 

 momentum HH' must be communi- 

 cated to the body, that is a couple 

 whose axis is parallel to HH' must 

 act on the body. This may be made 

 evident experimentally by placing a 

 loop of string over the axis F of 

 a symmetrical top balanced on its 

 center of mass (Fig. 85) and pulling 

 on the string. The axis of the top, 

 instead of following the direction of 

 the pull P moves off at right angles 

 thereto, although the string can only 

 impart a force in its own direction. 

 The pull of the string, together with 

 the reaction of the point of support 

 constitute a couple, whose moment 

 is perpendicular to the plane of the 

 string and of the point of support, 

 and it is in this direction that the 

 end of the axis, or apex of the top, 

 moves, as is required by the theory. 

 This simple experiment and the theory which it illustrates will make 

 clear most of the apparantly paradoxical phenomena of rotation. We 

 may describe it by saying that the kinetic reaction of a symmetrical 



Fig. 85. 



