An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.

ROTATION ABOUT A FIXED AXIS

15

If the plane YOX were not fixed in space, but revolving
dO
about OY, then wc, if measured by j, would be the angular
velocity of the body relative to the tlane YOX and not "the
angular velocity of the body."
Angular acceleration is the rate of increase of angular velocity.
Pljf^^<^-ane^fiixedlzn S acel Plane cxedn Space.
x
FIG. 5.
6. Torque. A force, or system of forces, capable of turning
a body about any axis is said to be, or to have, a torque
about that axis. It is measured by the moment of the forces
about the axis.
7. Uniform angular acceleration. If a rigid body is rotating
about a fixed axis with uniforrm angular acceleration a, then
after a time t it is clear that, supposing the initial velocity to
have been o), the final velocity
= W + at...............................(1)
It is also clear to those familiar with the elementary formulae
of particle dynamics, that if in time t, the rigid body under
the same conditions turns through an angle 0, the average
velocity at which this angle is described is
2 + o
0= + t
2
2
= ot + - at.........................(2)
Combining equations (1) and (2) as in particle dynamics
we obtain 2 1+
weQ2 = o2 + 2a0....................... (3)
These formulae are exactly analogous to the similar ones
relating to the rectilinear motion of a particle under uniform
rectilinear acceleration; for they are obtained from exactly