148] PLANE REPRESENTATION OF DYNAMICAL PROBLEMS. 137
but, by geometry, KA = ^, . OA, OA
whence, § 63, KI.HO'.OA' WOC HO.HA'. OA’ KI. OA' X O'A'. HA" QC — ' , w?
which is the required result.
148. Energy acquired by an Impulse.
The kinetic energy acquired by a given impulse, using the same notation
as before, is (§ 91) proportional to
Let A be the impulsive screw, and A' the screw about which the body
is constrained to twist. Draw the chord AOH (Fig. 30), then, as A' varies,
Fig. 30.
while A is fixed, the virtual coefficient of A and A' varies as A'H (§63).
The square of this is proportional to A'T, the length of the perpendicular
from A' on the tangent at H. If _PQ be the axis of inertia, the value of ua*
is proportional to the perpendicular A'Q, and, accordingly, the kinetic energy
acquired is proportional to
A'T
A'Q'