1D50.20 Centripetal Force Apparatus
the Whirligig
Abstract
A whirligig is used to demonstrate circular motion as well as the relationship between angular forces and linear
forces. By holding the whirligig by the glass tube and causing the ball to rotate in a circle the mass on the end
of the string can be raised. In order for the position of the raised mass to remain stationary the centrifugal force
experienced by the ball must be the same as the force of gravity experienced by the mass. By altering the mass
on the end of the string, the mass of the ball, the period of the rotation, or the radius of the rotating ball, it is
possible to observe how these variables are dependent on each other.
Picture
Safety Concerns
Use caution when stopping the whirligig, as the ball can hit the operator. To prevent injury when stopping
the whirligig, simply pull the weights (washers) towards the ground until the ball has halted atop the glass tube.
Equipment
• Whirligig with washers
• Whirligig with yellow coloured lead mass
• Whirligig with red coloured lead mass
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Procedure
Hold the Whirligig by the glass rod, and rotate the rod in a circular pattern until the mass begins to lift up. By
causing the ball to rotate at a constant velocity the mass should remain stationary. To stop the rotating ball pull
down on the mass slowly until the rotating ball comes in contact with the glass rod. If using the variable weight
Whirligig add or remove washers to increase or decrease the velocity of rotation of the ball at a given radius.
Theory
The mechanics of the Whirligig can be analyzed by considering the forces acting on the two objects on either
end of the string. All of these forces have been included in Figure 1 which is a free body diagram of the system.
R
vT
m
FC
Ball
Glass Rod
Lead Mass
M
Fg
Figure 1: Diagram of the circular path and the forces acting on the ball and lead mass.
If the mass has been raised above its original position and its position is stable, then the force of gravity acting
on the ball must be equal to the centrifugal force experienced by the rotating ball. The force of gravity acting on
the mass is simply given by Newton’s Second Law,
Fg = M g,
(1)
where Fg is the force of gravity on the mass on the end of the whirligig, and M is the magnitude of the mass.
The centrifugal force experienced by the rotating ball is given by,
Fc =
mv 2
,
R
(2)
where Fc is the centrifugal force in the ball, m is the mass of the ball, v is the angular velocity of the ball, and
R is the radius of the circular path of the ball. The angular velocity of the ball is given by,
v=
2πR
,
T
(3)
where T is the period of the rotating ball. By equating Equations 1 and 2 and by substituting in Equation 3,
an expression is found that relates the radius of the cirular motion with the period of rotation for the two given
masses. This expression is rearranged to obtain the equation,
s
4π 2 Rm
T =
(4)
Mg
2
Equation 4 gives an expression that describes the effect of altering either of the masses. It also predicts the
effect of changing the period of rotation.
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References
[1] G. D. Freier and F. J. Anderson. A Demonstration Handbook for Physics, ”Mm-2 Centripetal Forces”.
American Association of Physics Teachers One Physics Ellipse, 1996. pg M-29.
[2] Richard M. Sutton. Demonstration Experiments in Physics, ”M-138. Measurement of Centripetal Forces”.
McGraw-Hill Book Company, Inc, 1938. pg 61-62.
[3] John H. Walters Jr. ”Centripetal Force Apparatus”. American Journal of Physics, 29, March 196. pg 212.
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