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# The Motion of a Pendulum with a Top

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## 曜 小林

on 16 January 2014

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#### Transcript of The Motion of a Pendulum with a Top

The Motion of a Pendulum with a Top
1Y12B0391 Yoh Kobayashi
Introduction
Background
Experiment
Results
Discussion
Conclusion
References
sample
Pendulums and tops are
common object of physics.
What will happen if
they are connected?
Simple pendulum
When the swing is small...
The period is constant.
isochronism
(Toda, 1982, p.43)
Pendulum with large swing
The period (T) will be longer as the swing gets larger.
(Otani, 2011, p.5-7)
Top
A spinning top does not fall down, and the pivot rotates around the vertical line.
Precession
(Toda, 1982, p.184-187, Goldstein et al, 2000, p.275-295)
Hypothesis
The period of the pendulum connected with a top gets longer as the swing increases.
The spin of the top will probably influence the result.
A propeller was used instead of a top.
The propeller was spun with a motor. (Current: DC 3.0[V])
The pendulum was held at the initial angles and released quietly.
The initial angles were changed from 30° to 150° by 30°.
The period was measured ten times with each angle and the mean value was taken.
The use of the propeller causes unnecessary wind.
In order to examine the influence of the wind, the direction of the rotation was reversed:
First: clockwise (Experiment 1)
Second: counter clockwise (Experiment 2)
The period got longer as the initial angle increased whether or not the propeller was spinning.
The period increased less rapidly when the propeller was spinning.
There was not significant difference between the results with reverse directions of the spin.
The result basically confirmed the hypothesis.
The spin of the top (propeller) worked to moderate the change of the period caused by the change of the initial angle.
The effect of wind caused by the propeller was not significant.
Probably because its directions were always vertical to the motion of the pendulum.
The research suggests that the spin of the top works to moderate the change of the period of the pendulum.
Further research should be more accurate and should include theoretical approach (analytical dynamics).
Experiment is a useful way to confirm our knowledge.
「埼玉工業大学 機会工学学習支援セミナー (小西克亨) 単振子の振動の近似解と厳密解 (2013)」Accessed at
http://www.sit.ac.jp/user/konishi/JPN/L_Support/SupportPDF/SimplePendulum.pdf
on 16th January, 2014
Goldstein, H., Poole, C., and Safko, J. (2000). "Classical mechanics 3rd edition". San Francisco: Addison Wesley. (Japanese translation: translated by Yano, T., Ezawa, Y., and Fuchizaki, K. (2006) Kyoto: Yoshiokashoten)
Otani, M. (2011). 「常微分方程式論」[The theory of ordinary differential equation], Tokyo: Saiensusha.
Toda, M. (1982). 「力学」[Mechanics]. Tokyo: Iwanamishoten.
Thank you for listening!
Appendix
In the early stage of the research, a tire for toy car was used as the top.
However, it easily came off and the experiment failed.
The tire
The propeller
This is one of the funny failures...
Full transcript