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Transactions of the Wisconsin Academy of Sciences, Arts and Letters
volume IV (1876-1877)

McMurphy, J. G.
Rotation as a factor of motion,   pp. [235]-240 PDF (1.5 MB)


Page 237


Rotation as a Factor of Motion.
with the velocity of translation the deflection from a perpendicu-
lar will be very great and vice versa.
  When the ball is propelled against the vertical plane at any
other angle than a right angle with a rotary motion besides, the
problem  becomes somewhat more complicated.  Let the ball
be propelled from a          A                           B
with a positive rota-
tion. By its motion of
translation it ought
to rebound in the
path which makes            D       c                _C
the angle of reflec-   /
tion, equal to the   /d
angle of incidence  /a
But by its rotation    _      _     _      _    _
against the fixed point, b, it would tend toward c; hence it
will take the direction b-e, and be measured by the diagonal
parallelogram of forces, represented by b-a and b-c.  Here it is
plain that the angle of reflection is much less than the angle of
incidence. If the rotation be a negative or left-hand rotation
from the same point, a, following the same path, a-b, the result-
ant will be nearer a perpendicular - that is, the angle of reflec-
tion will be greater than the angle of incidence.
  If a ball be thrown perpendicularly against a vertical plane sur-
face with a positive rotation it will rebound to the left, if the rota-
tion be negative it will rebound to the right, if the rotation be for-
ward the ball will rise, if backward it will fall. If the ball be
thrown obliquely to the left, with positive rotation, the angle of
reflection will be less than that of incidence. If thrown obliquely
to the right, with same rotation, the angle of reflection will be
greater than that of incidence. The combinations are almost in-
finite, and afford a variety of valuable observations.
  There are some very curious and interesting experiments in
compound direct motion. If a ball lying upon a plane surface be
struck by a mallet so as to produce translation with forward rota-
tion on its horizontal transverse axis, and at the same time a ro-
tation about a vertical axis, the ball will neither rotate upon the
237


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