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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 236

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236     Wisconsin Academy of Sciences, Arts, and Letters.
be placed upon it and propelled perpendicularly against the ver-
trical plane by a blow, which takes effect above its center of grav-
ity. Such a blow will impart to the ball a rotary motion, together
with an onward motion or translation. When the ball reaches
the vertical plane its rebounding force, due to translation, will tend
to make it retrace its path, while the force due to its rotation will
tend to make it climb the vertical plane. It is actuated by the
resultant of these two forces, and rebounds through the air, in
the plane of those forces following the diagonal of the rectangle
of forces.
The following diagram* may serve to make the explanation more
apparent: Let A, B, C, D, be the vertical plane; C, D, E, F, the
horizontal plane;           A                            -
Let a be the point
from  which the
ball d is propelled                   C
on a-b; the ball
having a forward      -     D--C
rotary motion; b-d           /X
the distance the
ball would re-
bound by virtueE                               F
of its rectilinear motion; b-c the distance it would climb by vir-
tue ot its angular motion. Then will it be found somewhere on
the line b-e. Being a rectangle of forces, the resultant may be
expressed by the formula b-e = 4/(bc)2+(b-d)2.
If the ball is propelled from a point to the right of its center
of gravity, and constrained to keep the same perpendicular course,
it will have a negative or left-hand rotation ; when it strikes the
vertical plane it will not return in the same path, but will be re-
flected to the right, so that the angle of reflection is not equal to
the angle of incidence. But just as before, the path of the re-
turning ball is the resultant of two forces acting at right angles
to each other. If the angular velocity is very great, compared
*No cuts having been furnished by the author, the printer has been obliged
to construct the
accompanying figures, which are necessarily very imperfect.

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