876 APPENDIX B. A RIGID BODY ROTATING ABOUT A POINT

and in what direction the disc is spinning about this axis. If the disc were spinning veryfast we would have ω3 (t) very large. The other terms of angular velocity, ω1 (t)e1 (t)+ω2 (t)e2 (t) , yield a vector which is in the plane determined by e1 (t) and e2 (t) and so it is ameasure of the angular velocity about this axis. If we assumed ω ′i (t) = 0 for each i= 1,2,3,and ω2 and ω1 are moderate, note that we would still have substantial components oftorque, Γ2 (t) and Γ1 (t). Much more could be said about this problem and more examplescould be given but this much will suffice here.