Gyroscopes Consider a top or a gyroscope rotating as shown here. As long as the top or gyroscope rotates fairly rapidly about its axis of rotation, whatever other rotation or movement it may have will be minor and the angular momentum

Lwill line up with this axis of rotation. As the top or gyroscope slows down and eventually comes to a stop, of course, this will no longer be true.What torque acts on this top or gyroscope? Mainly, what

directionis the net torque acting on the top or gyroscope? And, then, we will want to ask whateffectthis has on the gyroscope -- that is, what happens to the gyroscope?Two forces act on the top or gyroscope -- the normal force

nthat supports it and the weight Mgacting downward. What torques do they produce? Simply from convenience, wesay"what is the torque?" but we alwaysmean"what is the torqueabout some reference point?". The point of contact or the point of support seems like a reasonable point to use. About that point the normal forcenproducesno torque. The weight, Mg, does produce a torque. If the x-, y-, and z-axes are oriented as shown (with the x-axis comingout ofthe page), then the torque, fromis a vector pointing along the positive y-axis (or to the right). That is the

onlytorque so it is certainly thenettorque.We also know the

net torquecauses the angular momentumLtochange,or

from which we can immediately find the

changein theangular momentum,To emphasize the

vector natureof all of this, we can write this asAs we noted earlier, the torque is a vector that points to the right. This means the

changein the angular momentum also points to the right.How does the angular momentum

Lmove so that thechangein the angular momentum is to the right? Thechangein the angular momentum isperpendicularto the angular momentum so themagnitude does not change. But thedirectionchanges. The angular momentum vectorL"precesses" or rotates as shown in the diagram above. The top or gyroscope, too, precesses so that its axis of rotation remains aligned with the angular momentumL.Here are additional examples or diagrams:

Conservation of Angular MomentumSummaryReturn to ToC, Ch11, Rolling Motion(c) Doug Davis, 2001; all rights reserved