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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 [235]


DEPARTMENT
                            OF THE
    MATHEMATICAL AND PHYSICAL SCIENCES.
        ROTATION AS A FACTOR OF MOTION.
                BY PROFESSOR J. G. McMURPHY, KENOSHA.
  When an elastic ball is thrown against a plane surface it re-
bounds from that surface according to certain fixed laws. Its
position at any moment will depend on certain conditions. The
elasticity of the ball, the angle of projection, the rotation of the
ball on its own axis, the velocity, will all of them affect the re-
bounding of the ball. Velocity and elasticity affect the distance
to which it will rebound; the angle of projection and angular mo-
tion will affect the direction of rebounding.
  A ball projected perpendicularly against a plane'surface will re-
bound in the same line, making due allowance for the attraction
of gravitation, which finally comes and controls its motion. The
resistance of the air is no inconsiderable factor. (In point of fact,
it is the latter only which is opposed to the force with which the
ball rebounds, for gravity acts at right angles to this force and is
not opposed to it.)
  If the ball, without rotation, is projected against the plane sur-
face at any angle, excepting ninety degrees, it will rebound so
that the angle of reflection shall be equal to the angle of inci-
dence; modified, of course, by gravitation and the resistance of
the air.
  Let us add another factor and examine the result. Given a horn-
zontal plane surface in front of the vertical plane. Let the ball


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