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02 Conical Pendulum

Aim

To show that the period of motion of a conical pendulum changes only noticeably at large angles.

Subjects

Diagram

.

Figure 1:.

Equipment

Presentation

  1. Set up the conical pendulum as shown in the diagram. Place the small paper circle under the pendulum and make the pendulum swing conically along the circumference of the paper circle. Measure the time needed for 10 periods. Repeat this procedure, but now with the large paper circle. In our setup, the times measured are 18.2 and 17.5 seconds, respectively.

  2. Take the small simple pendulum by hand and make it swing conically. Gradually increase its speed. At very large angles, the increase in angular velocity becomes easily noticeable.

Explanation

Theory tells us that 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}

The table in 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 \%. So only 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