Let α denote the angular velocity with which the plane of axes AB rotates about the fixed axis A. Then it is evident that
vB = α·AB,
(5)
and consequently that
α = γ·TB/AB.
(6)
For internal rolling, as in fig. 92, AB is to be treated as negative, which will give a negative value to α, indicating that in this case the rotation of AB round A is contrary to that of the cylinder bbb.
The angular velocity of the rolling cylinder, relatively to the plane of axes AB, is obviously given by the equation—
| β = γ − α |
| whence β = γ · TA/AB |
(7)