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02 Conical Pendulum

Updated: 09 Jul 2026

Aim

Showing that the period of a conical pendulum changes only noticeably at large angles.

Subjects

Diagram

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Figure 1:.

Equipment

Presentation

  1. Set up the conical pendulum as shown in Figure 1 . Place the small paper circle under the pendulum and let the pendulum swing conically along the circumference of the paper circle. Record the time required for 10 periods. Repeat but now with the large paper circle. Our recordings yielded respectively 18.2 and 17.5 seconds.

  2. Now, take the pendulum by hand and make it swing conically and slowly increase its speed. The increase in angular velocity becomes easily noticeable at very large angles.

Explanation

The period ( TT ) of a conical pendulum is given by T=2πlcos⁡ϕgT=2 \pi \sqrt{\frac{l \cos \phi}{g}} (see Figure 2).

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Figure 2:.

So T∝cos⁡ϕT \propto \sqrt{\cos \phi}

Table 1 shows that from 0∘0^{\circ} to 30∘,cos⁡ϕ30^{\circ}, \sqrt{\cos \phi} only changes 7%7 \%, while from 60∘60^{\circ} to 89∘89^{\circ} this change is about 82%82 \%. Hence at large angles ϕ\phi, TT changes noticeably.

Table 1:table

φ(%)\varphi(\%)cos⁡φ\sqrt{\cos \varphi}
01
150,98
300,93
450,84
600,71
750,51
800,42
850,30
890,13

Remarks

.

Figure 3:.

Sources

1D50 Central Forces
01 Going Round in Circles
1D50 Central Forces
03 Centripetal Force