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Demos: 1S-05 Rocking Meter Stick

A meter stick is laid across a cylinder and two 200-g weights are placed at equal distances from the middle of the stick. The cylinder has a sufficiently large radius such that the stick will balance in stable equilibrium. Tipping the stick slightly gives rise to stable oscillations. Referring to the diagram above, we can see that if we consider the motion a pure rotation about the instantaneous point of contact, the restoring torque, to first approximation, is m g (R - h) q. The equation of motion is

which leads to simple harmonic motion of period

The value of I is easily changed by moving the weights along the stick. Note the dependence of the period on R. If R > h, the system is stable. If R = h, the system is neutral. If R < h, the system is unstable. With a standard meter stick and 200-g weights, h is about 2.5 cm. If the cylinder has a radius less than this value, it will not be possible to balance the system.

Directions: With the two weights at the ends of the meter stick, place the stick on the larger cylinder, making sure that the point of contact is at the 50-cm mark. By moving the weights inward, the period can be shown to decrease. Then place the system on the smaller cylinder and show the instability.

Suggestions for Presentation: Remind the students that if the center of gravity of a system is above the support point, this generally leads to unstable equilibrium. Point out that the center of gravity of the meter stick plus weights is above the contact point. Can this system be stable? The key difference here is that the contact point moves as the stick is displaced. Then show that whether THIS system is stable depends on the relationship between R and h.

Applications: None that are apparent.

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Last Updated: May 9, 2016 11:44 AM

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