The Anderson intelligencer. [volume] (Anderson Court House, S.C.) 1860-1914, 1883-11-15
Anderson gntelli9enter.
Problem of the Wheel.

The following question has been much
discussed and various conclusions arrived
at; let us see if we can not settle 1t.
docs the upper part OF a wagon
wheel move faster than the lower part,
and if SO, how much faster?'
The correct answer is: The lowest
part does not move at all the highest
part moves forward twice as fast rs the
wagon. ] propose two demonstrations Of
this proposition:
FIRST DEMONSTRATIONS.
The lowest part of the wheel is in
contact with the ground hence, can
have no motion unless it be Il sliding
motion. a sliding motion might be pro.
duced by friction 1t the axle..ree or else.
where, but the consideration Of friction
evidently does not enter into the prob
lem. Now, il is plain that when this
part ceases TO be in contact with the
ground then it ceases to be the lowest
part; therefore, the lowest part OF the
wheel has no motion. Next, since we
have found point in the wheel which
docz not move, and which wc will call
the fixed point, it follows that all motion
Of the other parts must be circular mo-
tion about this point As center. Also,
the velocity of any part must be proper
toned to is distance from this point,
and its direction that of n tangent to the
arc which it is making.
Again the velocity of the center Of
the wheel asg the same as that Of the
wagon, for, being the same point rs the
center Of the axle, it can not move faster
nor slower nor in any other direction
than the axle. It's distance from the
fixed point is evidently equal to the
radius Of the wheel. Therefore, the
velocity Of any part Of the wheel must
be greater or less than that of the wagon
in proportion as its distance from the
lowest point is greater or less than the
radius OF the wheel, and the direction OF
its motion is at right angles to the dircc-
tiOn Of that lowest point. Now, the
distance Of the highest part is twice that
of the center; therefore, it moves twice
as fast {; tina. is, twice ~ fast as the wagon.
The direction of the lowest part is yer.
tical therefore, the direction of motion
SECOND DEMONSTRATION.
The wheel may ho regarded, as having
two motions-One its revolution about its
axis, the other its forward motion with
the wagon; by the composition Of these
two the actual motion of any part may
be found The forward motion Of the
wheel, as whole, would be seen by pre-
venting its revolution by locking the
wheel; it is the same III that of thu
wagon, both in direction and velocity
To examine its motion due to the rcvo
luton, let the y q ION stand still let th'
wheel be lifted by support under th'
axle; then cause the wheel to rcyolvt
with tho same frequency and in the sam,
direction rs when tho wagon was i'll mo
ton. Suppose, moreover, that th
wagon was headed northward, and th,.
we stand on its east side. Now, it vii
be granted that the outside of the whcc
moves with the same velocity as The
wagon did, the highest part northwar,
the lowest part southwark. Call north
ward motion plus, southwark motion
minus, and let the velocity of the wagol
be /. For tho lowest part of the wheel
the motion due TO revolution is minus !
that duo to the forward motion of th
whole is plus !. Combining these mo
ti0ns the algebraic sum is nothing, tha
is, the lowest part has no motion. Fo
the highest part the motion due to rcvo
luton 10 plus /, that due to forward mo
tion Of tho whole is plus l. The sum i
plus 2; therefore the actual motion i
forward with twice the velocity of th
wagon.
BY applying the principle of tho par
allelogram of forces, the actual motiol
Of any other point in the wheel may b,
readily found. The simplest cases, mex
to those of the given question, arc those
of the foremost and the hindmost part
of the wheel. The motion of the fore
most part is at an angle Of forty fv
degrees. downward, and with the velocit,
1.4l. The motion Of the hindmost par
is the same velocity at al angle OF forty
five degrees downward Courier -Journo!